Dr. Crawley is an Assistant Professor, Mr. Poublanc is a Research Assistant, Mr. Ferrari is a Research Assistant, and Dr. Roberts is an Associate Professor in the Department of Medical Imaging, University of Toronto and University Health Network, Toronto, Ontario, Canada.

Perhaps no techniques better exemplify the successful transition from laboratory experiment to clinical routine than diffusion and perfusion-sensitive magnetic resonance imaging (MRI). Little more than a decade ago, these techniques were the exclusive province of esoteric physics. Yet, they have emerged as an invaluable asset to the neuroradiologist and neurologist alike; in some sense they can be considered to be at the forefront of the movement toward physiological, or functional, imaging. The purpose of this article is to review the physical basis of the techniques, to discuss their implementation and future potential, and to consider their principal application in the diagnosis and, importantly, characterization of acute cerebral ischemia.

Diffusion and apparent diffusion

Like all fluids, water molecules undergo continual random motion (so-called Brownian motion) at a rate described by the self-diffusion coefficient, D, and the (lesser-known) Einstein equation (<L ² > = 2D*). This motion arises largely because of the thermal energy possessed by the molecules being expended as kinetic energy and, thus, creating movement. ¹ If the position of a particular molecule is known at a given time, the Einstein equation predicts the expectation value of the molecule's displacement (L) at a later time (*), based on the value of the self-diffusion coefficient, D. Using paired magnetic field gradient pulses to effectively encode, and then subsequently decode, spatial position, the degree of water displacement, or diffusion, can be estimated in MRI, via the relative ineffectiveness of spin-echo formation (and thus the signal loss on such a diffusion-weighted image [DWI]) ^2-5 (Figure 1).

Formally, the signal intensity observed on a DWI is approximated by the expression S * e ^-bD , where the factor b relates to the degree of diffusion sensitivity of the sequence. ⁶ Consider a T2-weighted MRI--the value of echo time (TE) effectively determines the sensitivity of the sequence to the process of T2-relaxation; analogously the b-value determines the sensitivity of a DWI to the process of diffusion: sequences with low b-values are relatively insensitive to diffusion; sequences with high b-values are sensitive to even minor water displacements. Typically encountered bvalues in clinical practice are of the order of 1000 sec/mm ² . From observing the signal obtained with different b-values (typically b = 0 and b = 1000 sec/mm ² ), it is thus possible to estimate D. However, if it were truly water self-diffusion alone, this would be of rather limited biomedical interest­­the self-diffusion coefficient of a molecule depends on its molecular weight, which is constant for water (18) and the absolute temperature, T, which is also of rather limited variation in vivo (310 K, 37°C). In fact, however, the physicochemical microenvironment of tissue prohibits free self-diffusion. Consequently, the parameter we derive from the above analysis is referred to as the apparent diffusion coefficient (ADC), which is related to microviscosity, organelle, membrane and molecular interactions, active transport mechanisms, perfusion, bulk flow, and, of course, the ensemble averaging of the many different water environments contained within an imaging voxel. ⁷ By its nature, ADC is also extremely sensitive to gross movement of the patient. Nonetheless, if gross motion is minimized (by physical restraint and ultra-fast imaging), derivation of the ADC yields tantalizing insight into water molecule displacements on a micron (µm) scale, several orders of magnitude smaller, in fact, than the nominal pixel, or spatial, resolution of the image.

Anisotropy

Furthermore, while self-diffusion is an isotropic process (ie, there is an equivalent likelihood of molecular displacement in any given direction), apparent diffusion may well exhibit a directional preference (consider, for example, a cylindrical microstructure in which motion is permitted along the long axis, but impeded in the cross-sectional plane). Such directional preference is termed anisotropy and is a characteristic feature, for example, of white matter tracts in the brain. Anisotropy can be revealed via diffusion-weighted MRI by conducting separate experiments in which diffusion sensitivity or positional encoding/ decoding is applied in successive experiments in different directions (eg, by first using the x-axis gradients to encode displacement in the x-direction, then subsequently the y-axis gradients, and so on). ^7-9 In fact, the degree of anisotropy and its preferred direction (an example used by Prof. Jim Provenzale, Duke University Medical Center, is to consider the shape of an American football versus a soccer ball) can best be estimated by performing such directional displacement encoding in multiple (>= 6) directions and describing the diffusion process as a 3 * 3 matrix, or tensor ¹⁰ (Figure 2). Since this analysis can be performed on a voxel-by-voxel basis it is, thus, possible to ascertain for each image voxel both the degree of anisotropy (how elongated is the football) and its preferred direction (which way is it pointing). Recent sophisticated postprocessing techniques have used these properties to follow the arrows and essentially reconstruct the fibers of white matter tracts. ¹¹

Diffusion in stroke

However, the predominant clinical indication for diffusion-weighted MRI remains the diagnosis of acute cerebral ischemia. ^12,13 While the pathophysiologic mechanisms underlying the diffusion changes remain the subject of debate, a simplistic description of the process is offered below: Arterial occlusion or sustained severe stenosis leads to hypoperfusion of the subserved vascular territory. Subject to such deprivation of essential nutrients, energy-requiring cell membrane transporters (particularly the Na ⁺ /K ⁺ -ATPase pump) begin to fail. The cells thus lose the ability to regulate their volume and there is an influx of extracellular fluid into the intracellular space­­the cells swell, a condition referred to as cytotoxic edema. Whether diffusion is reduced because of reduced fraction (and increased tortuosity) of the relatively free diffusive environment of the extracellular space, or because of the increased volume fraction of the slower diffusive environment of the intracellular space, or because of reduced activity of membrane transporters due to energy deprivation, or all of the above, the net consequence is that the ADC may be reduced by up to 50% within minutes of the insult. ^14,15 As a consequence of reduced freedom of diffusion in this ischemic territory, the region appears characteristically relatively hyperintense in comparison with healthy tissue on diffusion-weighted MRI (Figure 3). It is worth noting that a DWI formed by the application of pulsed gradients to a conventional spin-echo or spin-echo echoplanar imaging (SE-EPI) sequence incurs both diffusion and T2-sensitivity. Consequently, hyperintensity apparent on a DWI could, in principle, be attributed either to reduced diffusion, or simply to elevated T2 (so called T2-shine through). Consideration of a T2-weighted (but not diffusion-weighted) image (namely the control image acquired with b = 0) reveals the origin of the hyperintensity and construction of the synthesized ADC map (derived from two or more images with different b-values, typically b = 0 and b = 1000 sec/mm ² ) quantitatively eliminates any influence of T2-weighting. ¹⁶

In the absence of adequate intervention, the pathophysiologic cascade continues and cell lysis ultimately occurs, leading to the observation that the area of reduced diffusion visualized by DWI predicts the area of ultimate infarct. So, while DWI is sensitive to the tissue or cellular consequences of hypoperfusion, the root of the problem lies in the effective delivery of blood to the tissue. Consequently, DWI is commonly accompanied by techniques that attempt to visualize and characterize perfusion itself.

Perfusion

From a physiological point of view, perfusion is an intuitively easy concept to grasp; for any volume of tissue under consideration, a measure of perfusion should estimate the volume of blood that passes through the capillary bed per unit time. It is this volume of blood that delivers nutrients to the tissue, whereas blood that travels straight through the volume of tissue within arteries or veins should not be included in the measurement. Thus, importantly, perfusion is not exactly the same as blood flow. For quantitative work in animal models, radioactively labeled microspheres are injected into the blood in order to mimic this delivery mechanism to the tissue. The diameter of the micro-spheres is selected so that they become trapped within the capillaries and the level of radioactivity is subsequently measured for each tissue of interest. Any noninvasive MRI method should aim to achieve a similarly meaningful estimation of perfusion.

We have already shown how MRI can be made sufficiently sensitive to the random motion of water molecules across an applied magnetic-field gradient to enable the apparent diffusion coefficient of water within the tissues to be imaged. As a first step in directing the motion-sensitivity of the MRI signal specifically toward flow through the capillaries, gradient pulses with a relatively small sensitivity to diffusion (rather low b-value) were applied in order to measure the component of apparent diffusion of flow through the quasi-random tortuosities of the capillary bed. ¹⁷ In practice, a large number of scans over a range of b-values must be acquired in order to separate out this apparent diffusion component from the underlying smaller diffusion of the water molecules. Ultimately, the method is limited by the fact that the proportion of water within the capillary bed is only approximately 2%, making its contribution to overall apparent diffusion extremely hard to quantitate reliably above the noise in the images.

In a quite different approach, the problem of sensitivity has been solved by employing an intravenous (IV) bolus injection of gadolinium-based contrast agent that profoundly affects the signal (by up to 50%) on a gradient-echo (typically gradient-echo echoplanar imaging [GE-EPI]) scan as it passes through the vasculature. ^18,19 A power injector may be used to achieve a very tight bolus, so that the signal loss during the first pass through the tissue can be measured relative to an initial baseline by a high temporal resolution (approximately 1 to 2 sec) scan (repeated successively for a total scan time of approximately 1 min). Gadolinium is a paramagnetic substance, and in the chelated form in which it is employed as a contrast agent, it does not cross the normally intact blood-brain barrier (BBB) and, hence, remains intravascular within the brain. As the bolus passes through the blood vessels, a relatively large magnetic field difference is created between the gadolinium-doped blood and the surrounding brain tissue. The different magnetic fields within each voxel cause the MRI signal to dephase, producing a progressive signal loss (characterized by a time constant T2*) over the TE. A gradient-echo scan with long echo-time (approximately 40 to 60 msec) is referred to as a T2*-weighted scan and is the basis of the dynamic susceptibility contrast (DSC) approach to perfusion sensitive MRI ²⁰ (Figure 4).

This kind of scan is extremely sensitive to the local field inhomogeneities produced by the contrast agent, but this signal loss mechanism is not particularly specific to capillary vessels. Over the last several years, it has become somewhat more common to opt for a T2-weighted spin-echo scan, which produces a signal loss that mostly arises from the passage of gadolinium through the capillaries rather than through the larger blood vessels within the voxel. ²¹ Since the spin-echo refocuses static field inhomogeneity effects, the only remaining signal loss mechanism is that due to water diffusion through the susceptibility gradients. Since there is a limited time window (ie, the TE) for this process to occur, the spin-echo scan will be sensitive only to susceptibility gradients that are significant over the short distance that a water molecule diffuses during the TE. This corresponds fairly closely to the susceptibility effect around a gadolinium-containing capillary. Nonetheless, this capillary specificity is obtained at the expense of sensitivity, and typically SE-EPI signal losses are considerably smaller than those observed using a GE-EPI sequence, prompting the use of higher doses (eg, 0.2 to 0.3 mmol [Gd]/kg) of contrast agent.

Since the contrast agent remains within the vascular space, it is not surprising that this dynamic bolus method measures blood volume more directly than it can measure perfusion. In fact, for a given quantity of contrast agent passing into the region of interest, the relative blood volume is basically given by the area under the curve representing signal loss as a function of time (after rescaling of signal intensity to concentration proportionality). ¹⁹ This is intuitively obvious: if the bolus is more spread out in time, the signal loss curve will also be more spread out over time but the peak signal loss will be correspondingly less, and the area under the curve will remain the same. Clearly, as long as the blood vessels are intact and are not totally collapsed, one may refer to a histologically meaningful blood volume even when there is no actual blood flow into the tissue. Therefore, while the measurement of blood volume is useful in terms of issues such as vascular resistance, on its own it says nothing about whether blood is actually reaching the tissue.

If the gadolinium could be injected instantaneously into the arterioles supplying the capillaries, then the temporal behavior of the tracer concentration curve (specifically the mean transit time [MTT]) would provide the necessary information for a calculation of the volume flow rate (ie, perfusion) through the capillaries. ²² Specifically, the central volume principle states that perfusion (volume of blood/time) = blood volume/MTT. ²³ Unfortunately, the IV bolus requires several seconds of injection time (typically 2 to 5 sec) and is then dispersed somewhat as it travels through the heart and pulmonary circulation, so that its breadth may be as much as 10 sec prior to entering the tissue of interest. This arterial input function (AIF) can be measured from the tracer concentration curve within an appropriate artery inside the imaging volume. A mathematical deconvolution is then required to attempt to remove the temporal blurring caused by the prior dispersal of the bolus. ²⁴ Unfortunately, the MTT through each voxel is short compared with the prior blurring (dispersion) of the bolus, so it is hard to achieve accuracy in the measurement of either the MTT itself or thus in the derived estimate of perfusion.

In spite of the fact that a quantitative measure of perfusion is hard to achieve with the dynamic bolus method, it is widely used in clinical practice because it offers rather robust qualitative and indeed semi-quantitative indicators of perfusion. ^25,26 We noted above that the direct measurement of blood volume may be rather irrelevant to the evaluation of a tissue's perfusion status. Referring again to a situation in which there is some finite blood volume but little actual movement of blood through the tissue, it is clear that the dynamic bolus scan will register little or no signal loss within this tissue, because the bolus will barely arrive at or pass through its capillaries. For the general case of reduced perfusion through ischemic tissue, the whole time-scale of the arrival and local dispersal of the bolus will be spread out. It will then become more difficult to detect any measurable area under the tracer concentration curve even if the bolus completes its passage through the tissue within the duration of the scan, since a relatively small signal loss occurring over a long time is much harder to distinguish from other causes of temporal drift in the MRI signal. Therefore, in the presence of local ischemia, the area under the tracer concentration curve provides a measure of blood volume that becomes heavily weighted by some perfusion factor when perfusion to the tissue is severely compromised.

This still leaves a lack of sensitivity for mild to moderate perfusion deficits, where the dynamic bolus method is able to measure the blood volume fairly accurately. In this case there is little or no perfusion-weighting in the final blood volume image, which on its own may give little indication of any compromised blood flow into the tissue. We expect the tracer concentration curve to be delayed and dispersed in time relative to normally perfused tissue in the same subject. This should provide some useful information without explicitly requiring any deconvolution procedure. We note here that the purpose of the deconvolution method described above is to attempt to provide absolute quantitation of perfusion that would enable a measurement from one scan to be compared with measurements from other scans (obtained with contrast boli with different temporal profiles), or for the establishment and use of quantitative cerebral blood flow (CBF) thresholds for stratifying ischemia. In most clinical situations, the basic function of a diagnostic imaging test is to map out regions of pathology relative to more normal areas within the same individual. While it would be ideal to be able to compare measurements between scans, in practice, a more robust method can often be employed if one limits the scope of quantitation to relative measurements between tissues obtained within an individual scan. This is certainly the case with the dynamic bolus method, since for a relative measure of perfusion, the MTT can be calculated from the tracer concentration curve without the need for deconvolution, at least assuming all tissues within the imaging volume experience the same AIF. ²⁷ This also obviates the dilemma of arterial selection (since different arterial input functions may be obtained in different representative arteries, leading to different quantitation of perfusion parameters).

Arterial spin labeling

Another technique offers the promise of quantitative cerebral perfusion imaging without the need for exogenous contrast agents (Figure 5). Although not yet in routine clinical practice, the technique (or rather family of techniques) known as arterial spin labeling (ASL) merits some discussion, especially in light of increasing field-strength MRI. It can be applied in situations where several separate perfusion measurements may be required (eg, during therapy). Arterial spin labeling techniques are plagued by nearly as many acronyms as gradient-recalled echo imaging (Table 1), but the techniques can be grouped into two distinct families: pulsed ASL (PASL) and continuous ASL (CASL).

A PASL sequence is obtained by sending a 180° radiofrequency (RF) pulse during a very short period of time to a large tagging slab (approximately 10 cm) just below the circle of Willis, proximal to the volume of interest, in order to label the water protons of the arterial blood by inverting their magnetization. While the blood is flowing into the arterioles and then the capillary bed, the magnetization of the arterial blood undergoes longitudinal relaxation. After a certain delay of time when the blood has transited to the capillary bed and has perfused into the brain tissue, an image is acquired using a fast sequence, such as echoplanar or spiral imaging. The experiment is then repeated without inverting the arterial water protons and the two images are subtracted to give a map that should show the amount of blood that has perfused the mass of tissue contained in a voxel during the time between the tagging pulse and the image acquisition. Since the absolute signal intensity difference between the two scans (with/without arterial inversion) is very small, multiple images are averaged together and the perfusion map is calculated using models that relate the difference of magnetization to the regional cerebral blood flow. ^28,29

A CASL sequence uses basically the same principle as a PASL sequence, except that in a CASL sequence the blood is continuously tagged (for approximately 3 sec) on a much smaller region (approximately 1 cm) and farther away from the imaging slices (a gap of approximately 10 cm between the two regions).

Problems and artifacts: Why quantitive ASL is not yet clinically routine

In fact, ASL entails many problems and artifacts that have to be reduced in order to realize the promise of accurate flow quantitation. Tagging of a separate label slice or slab can be considered as off-resonance excitation for the imaging slice. Consequently, it may incur magnetization transfer signal loss in the presence of appropriate macromolecular entities in tissue. ²⁸ Since ASL techniques require a subtraction of a tagged image from a control one, care must be taken to have the same magnetization transfer influence during both sequences (ie, the macromolecules irradiated by the 180º pulse during the tagging sequence must be similarly affected during the control sequence). This effect is more important for a CASL sequence because of the long duration of the RF pulse, whereas it is lesser for the PASL family. Typically it is addressed by applying downstream or irrelevant 180° RF pulses analogous to the tagging pulses, during the control image sequence. ^30,31

The uncertain transit time for the blood to flow from the tagging region to the imaging slice makes the quantification difficult. This may be ameliorated by lengthening the interval (inversion time [TI]) between tag and image in order to allow the assumption that all the tagged blood has perfused the slice before the acquisition. Lengthening TI also allows the arterial tagged blood to pass through and leave the imaging slice before imaging. Indeed, tagged blood flowing in arteries passing through the imaging slice at the time of acquisition would otherwise cause undesired focal high-intensity regions on the perfusion map. So, a long TI overcomes two artifacts; however, it also reduces the intensity of a signal that is already weak (since the tags fade during T1 relaxation ­ in the limit of TI ~ 5 * T1, tagged blood appears of course to have the same magnetization as the untagged blood of the control image, and subtraction of the two images yield nothing more than noise). It seems that this problem will be reduced in severity with the implementation of higher field-strength MR systems (where T1 relaxation times are longer). ³²

One also has to consider that the inversion profile of the tag may not be a perfect box, and, thus, incomplete inversion remains at the edges of the tagging region. In this way, a sequence called QUIPSS II (quantitative imaging of perfusion using a single subtraction) has been developed in order to control the time width of the tag or, in other words, the amount of tagged blood that enters the imaging slice. ^33,34 To do so, a saturation pulse is applied to the labeling region at time TI ₁ after the application of the label. In this case, there is a precisely known amount of labeled blood (equal to flow * TI ₁ ) that leaves the labeled region.

Comparison of DSC and ASL imaging

The most obvious difference between these two perfusion techniques (Table 2) is the fact that the gadolinium remains intravascular when the BBB is intact, while the magnetically labeled water molecules in the blood plasma diffuse relatively freely into the tissue. With radioactive labeling as used in H ₂ ¹⁵ O-positron emission tomography (PET) and ¹³³ Xe-single-photon emission computed tomography (SPECT) perfusion scanning, the slow washout of tracer from the tissue back into the vascular system and the slow radioactive decay of the tag together define a measurement time-scale that is much slower than the first pass dynamics of the DSC scan. ^35,36 However, in the case of magnetic labeling, the tag decays extremely rapidly (down to 37% of initial value in TI ~ 1 sec), so that the situation is dramatically reversed. Whereas the signal loss as the gadolinium bolus makes its first pass through the tissue's capillary bed is quite easily monitored using an echo-planar imaging (EPI) scan, the T1 decay of the magnetic label basically forces the ASL scan to be performed at a single inversion time (TI ~ 1.4 sec). This time corresponds to the optimal measurement time, given the competing effects of signal gain over time as labeled water enters the tissue versus signal loss due to T1 relaxation.

For absolute quantitation of CBF, the model of the tracer kinetics that is appropriate to the DSC method (nondiffusible tracer) really requires a local estimate of the AIF that is relevant to the tissue of interest. Since ASL uses a freely diffusible tracer, it should not have a fundamental problem with AIF variability. The equivalent PET and SPECT methods rely on an integration of the total tracer that is delivered to the different tissues to form a perfusion map that is independent of the local AIFs. It is only because the ASL measurement usually has to be performed before the trailing edge of the bolus of labeled spins has reached all the tissues of interest that a nominally similar problem arises. In some of the ASL variants, the trailing edge is not well-defined, but in the QUIPSS method, a saturation pulse is applied just below the imaging volume about 0.7 sec after the inversion pulse. ^33,34 This allows another 0.7 sec for the trailing edge of the now well-defined bolus (with time width = 0.7 sec) to reach all the tissues within the imaging volume.

From the point of view of systematic errors, ASL has the greater potential for absolute quantification of perfusion, but the level of the perfusion signal (approximately 2% of the raw signal) is extremely low relative to the noise, which will propagate a relatively large random error into the final CBF map. This is somewhat improved at higher field strength due to longer relaxation times, which enable a greater buildup of labeled protons to occur via the use of a longer inversion time. If the calculation of ratios of CBV and of MTT between ischemic and relatively normal tissue is adequate for assessment using DSC, then the main criteria for choosing between the two methods are the relative speed and excellent signal-to-noise of the DSC scan. Furthermore, typical ASL implementations are limited in the number of slice locations accessible compared with DSC methods, which typically provide 20 to 30 slices or whole-brain coverage. On the other hand, since ASL is noninvasive and the endogenous tracer literally disappears within a few seconds, these scans can be used repeatedly to monitor blood-flow changes during a vascular reactivity test using a vasodilator, such as acetazolamide or CO ₂ .

Reactivity

Ischemic tissue can maintain a reasonable CBF by dilatation of the precapillary resistance vessels, which causes an increase in CBV (hence the commonly observed normal or even elevated CBV measurement, despite ischemia). Eventually, this autoregulatory mechanism reaches some limit (referred to as the reserve capacity), and infarction is likely to occur. For a given vasodilatory challenge, there will be a significant increase in CBF in healthy tissue but much lower reactivity in tissue with an exhausted reserve. These studies were pioneered using transcranial Doppler ultrasound, and have become a fairly standard component of SPECT perfusion scanning. ^37-39 The feasibility of MRI reactivity scans has been demonstrated using both ASL and blood oxygen level dependent (BOLD) techniques ^40,41,42 (Figure 6). The latter uses a T2*-weighted EPI sequence (identical to that used in DSC imaging) and is sensitive to the susceptibility effect of deoxyhemoglobin, which is effectively an endogenous equivalent of the gadolinium used in DSC imaging. Interestingly, the BOLD susceptibility method also has problems with absolute quantitation of CBF, since the signal depends on the resting deoxyhemoglobin level, which depends on resting CBV, CBF, and oxygen extraction fraction (OEF). Recent studies have shown a strong correlation between reduced reactivity and increased MTT as measured by DSC imaging, ⁴³ and both measures are considered to be important in detecting tissue at risk of infarction.

Conclusion

Both diffusion and perfusion imaging techniques stand at the forefront of physiologically sensitive radiologic imaging, offering another tantalizing combination of integrated imaging of anatomy and function. Although the principal clinical indication is in the imaging of ischemia, applications are becoming more widespread and include a broad range of cerebrovascular diseases. Efforts to extract the maximal clinically relevant information from dynamic perfusion imaging center both on methods for accurate and precise quantitation of CBF as well as on intrinsic understanding of the co-varying behavior of separate perfusion parameters--CBV, delay of bolus arrival, etc. Surrogate estimates of the degree of collateral blood supply and distinction between good compensatory autoregulation and bad loss of vascular tone remain subjects of active research. The concept of monitoring vascular reactivity (ie, vascular function, not just vascular state) and indeed vascular integrity (via the extravasation of initially intravascular contrast agent, leading to estimates of microvascular permeability) ⁴⁴ offer considerable promise in the expanding clinical role of these methodologies. AR