MAGMA (1994) 2, 225-231
Perfusion and diffusion imaging J. v . H a j n a l a n d I. R. Y o u n g * Robert Steiner M R Unit, Hammersmith Hospital, London W12 OHS, UK
This article reviews the measurement of perfusion and diffusion and discusses the implications of the observed anisotropy of diffusion of water molecules in some tissues. An experiment is described which shows how observations of diffusion anisotropy can be used to obtain structural information for a model system and to estimate tissue properties in vivo. Differences between perfusion and diffusion are highlighted, and the impact of the former on temperature measurements in vivo based on MRI is discussed. The article concludes that the observation of these phenomena are worth very substantial effort in order to elucidate a number of quite significant problems in the practice of magnetic resonance imaging today. Keywords: perfusion, diffusion, anisotropy, measurement in MRI.
INTRODUCTION Although commonly discussed together, and frequency regarded as being phenomena that can be observed by similar techniques, perfusion and diffusion in tissue are really quite different. The former refers to flow through the fine (capillary) section of the vasculature. The capillaries have diameters which are too small to be resolved by conventional magnetic resonance imaging (MRI) and have been modeled as being quasirandom in orientation [1] although there is a tendency for those bringing in arterial blood to roughly parallel those removing veinous blood. Flow in any one capillary is, however, coherent, with typical flow rates of the order of millimeters per second. Diffusion is a microscopic phenomenon associated with thermally driven random motion. In the context of in vivo MRI it relates' to the movement of free water molecules inside tissues. Molecules in a free fluid move with equal probability in any direction at a rate that is determined by the diffusion coefficient, D, which has dimensions of length squared per unit time. The mean distance traveled by molecules in a time t is proportional to ~ and amounts to around 20 ~m in 80 ms for water at body temperature. Thus, on the time scale of a typical T2-weighted spin echo, mol* Address for correspondence: Robert Steiner Magnetic Resonance Unit, The Royal Postgraduate Medical School, Hammersmith Hospital, Du Cane Road, London W12 ONN, UK. 0968-5243 © 1994 Chapman & Hall
ecules diffuse mean distances that are comparable to cellular dimensions. As a consequence, tissue structure has a profound impact on the apparent diffusion of water in vivo as observed by MRI. Perhaps the most notable manifestation of this is the apparent anisotropy of diffusion observed in both white matter and muscle. This article discusses the measurement of perfusion and diffusion in vivo and the impact on the latter of anisotropy. An example is given of how diffusion anisotropy may be exploited to estimate the mean diameter of cylindrical barriers that may be associated with myelinated axons. Some observations of diffusion and perfusion in vivo are described, and some of the problems of understanding what is happening in the microcirculation are discussed.
CONVENTIONAL OBSERVATION OF DIFFUSION Measurement of diffusion in vivo has conventionally relied on the pulsed gradient spin-echo (PGSE) method of Stejskal and Tanner [2]. Although standard for early diffusion work [1, 3, 4], this technique has also been used for accurate flow measurement [5]. The form of this pulse sequence is illustrated in Fig. 1, in which sensitization to movement is created by extra gradient pulses (shown shaded), which in this case are in the direction normal to the plane of the slice. For coherent motion, this sequence results in a
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Slice select gradient
180o pulse
G
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l 9
time
A
Fig. 1. Diagram of the PGSE sequence, with motion sensitization (shaded regions) along the slice selection direction.
phase shift of the received signal rather than a change in amplitude. When the motion is random (as with molecular diffusion) the relationship established in Ref. 2 for signal acquisition after an echo time TE is applicable: S = S0 (1 - exp ( - ~IR)) exp
TE
2
2 2[
~
(1) tn this equation, S is the observed signal, So is the signal available after full recovery, TR is the repetition time, ~/is the gyro magnetic ratio, G is the gradient pulse amplitude, and ~ and A are times defined in Fig. 1. Equation (1) is generally written in compressed form S = SRexp (-bD)
(2)
where SR is the available signal taking T1 and T2 relaxation into account and b is a diffusion sensitivity parameter [1] defined by b = y2G2~(D-8/3)
(3)
The value of the diffusion coefficient D can be calculated in principle by measuring the signal for a range of values of b and fitting the data using Eq. (2). A minimum of two different b values is required for this, in which case 1
D - bB~
SA In S--~
(4)
where SA and SB are signals obtained with diffusion sensitivities bAand bB. Pixel intensities in images produced by the sequence in Fig. 1 are weighted by the local degree of diffusion of spins as specified by Eq. (2). In view of the extreme sensitivity of the PGSE sequence to subject motion, satisfactory images can only be obtained by MAGMA (1994) 2(3)
careful attention to motion control, including cardiac gating, or the use of single-shot techniques such as echo-planar imaging (EPt). The latter provides an attractive combination of ease of use and capability for rapid data acquisition but has generally not achieved the resolution available from more conventional approaches. For a simple fluid phantom the logarithm of the signal is found to decrease linearly with increasing b according to Eq. (2). However, in vivo it was observed that although this relationship appears to hold for moderate b values, it tends to fail both at high and low b values. The high b value behavior, in which the signal decays more slowly than expected, remains to be fully explained. For small b values, the signal rises above the straight log-linear curve and this is often attributed to perfusing blood, the signal from which is completely destroyed at larger values of b because it is undergoing relatively very fast motion. A further complication arises in some tissues as Moseley et al. were the first to point out [6] with their observation of anisotropy in the diffusion coefficient in white matter in cat brain. This remarkable phenomenon can be explained by supposing that molecules could diffuse freely along tubular structures such as axons but are prevented by largely impermeable walls from more than very restricted movement in a radial direction across them. Then, if b is held constant, but the time between the gradient pulses (A) is varied, initially, when A is small, signals tend not to display strong dependencies on the direction of sensitization. As A is extended, however, signals after sensitization transverse to the axons are generally much greater than those after sensitization along them.
USE OF DIFFUSION ANISOTROPY TO OBTAIN STRUCTURAL INFORMATION Diffusion anisotropy provides a means of studying microscopic tissue structure. Several theoretical models have been developed to describe the effect of restricting barriers of varying geometries. Tanner [7] considered arrays of parallel partially permeable planes, and Neuman calculated the signal from a PGSE for spherical and cylindrical impermeable barriers [8]. We have verified the applicability of Neuman's relationships using a microchannel plate. This is made of glass 0.5 mm thick, drilled with an array of nominally identical circular holes, 12.5 t~ in diameter, with a center-to-center distance of 15 V-- The pores in the plate were filled with water, and excess water was
PERFUSlON AND DIFFUSION IMAGING
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Diffusion Sensitivity Factor, b (slmm 2) Parallel
•
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Fig. 2. Results from a microchannel plate experiment showing the logarithm of signal from a PGSE sequence at 0.15T plotted against diffusion sensitivity (b). The two regression lines are for sensitization along the length of the pores (parallel) and transverse to them (perpendicular). The pore diameter was 12.5 t~m.
removed carefully from the faces of the plate. Results of PGSE measurements at 0.15 T are shown in Fig. 2, in which the logarithm of the signals obtained with sensitization normal to and in the plane of the microchannel plate are plotted against the diffusion sensitivity of the sequence. From this data the mean diameter of the pores was calculated using Neuman's formula to be 14 ~, which agrees quite well with .the actual value. In a study performed on the corpus callosum of a normal volunteer, the measurements were obtained under normal conditions at 0.15 T (Fig. 3). The apparent mean axonal diameter was calculated to be about 22 I~ [9]--again Ln(Signal) ~0,25
*0.75 -1 ~1,25 -1,5
-1.75 *2
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Diffusion SensitivityFactor, b (s/ram) a-~ L-R Fig. 3. Results comparable to those in Fig. 2 but for the corpus callosum of a normal adult volunteer, Points labeled L-R are for sensitization parallel to axons, those labelled A-P are for perpendicular sensitivities. On the basis of the results, the mean diameter of the mix of restricted intracellular and extracellular volumes of water was calculated to be 22 i~m.
0
!
0
20
!
!
40 60 G (mT/m)
!
!
80
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Fig. 4. Illustration to show the desirability of larger gradients for diffusion-weighted experiments. The curve is plotted for a b of 1000 s mm -2 to show the reduction in TE with increasing gradient strength. There is a minimum time overhead needed for RF pulses, spatial localization, and data acquisition !shown hatched), so that above around 40-50 mT m -1, increases in gradient strength become much less useful.
generally in accord with expected values if it is assumed that signals may derive from both intraaxonal and extraaxonal water.
EQUIPMENT ISSUES Diffusion-weighted sequences can be implemented on conventional machines and frequently are. Where measurement is needed, however, and large values of b (1000 s mm -2 or so) are required, gradient coils with strengths similar to, or greater than, those required for echo-planar imaging [10] are desirable. This is because although the diffusion weighting achieved for a given gradient strength can always be increased by extending ~ and d~, this is at the expense of increased TE--and results in substantial signal loss through transverse relaxation as well as diffusion weighting. Increasing peak gradient strength (for example, to 40 m T m - : ) allows large diffusion sensitivities to be achieved at relatively short echo times. Figure 4 is a plot of minimum echo time for a constant b of 1000 s mm -2 versus available gradient strength. It is noticeable that, with the sequence parameters employed, TE is markedly reduced in changing from 10 to 40 mT m -1 with more marginal reductions achieved beyond this value. MAGMA (1994) 2(3)
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~W
x bucking/# Cylindricalcoil Aentre of gradient/ former field coiI Fig. 5. Schematic diagram of an asymmetric gradient coil set, with attached bucking coils. Z is a conventional arrangement, but both X and Y (not shown) are folded back, and the unbalanced torques arising from this are compensated by the series-wound bucking windings.
Large gradients can conveniently be created by small insert gradient coils as most studies of interest are of the brain. However, the subject's shoulders restrict access to all except the top part of the brain with conventional gradient coil designs. One option is to use an asymmetrical system in which the Z-gradient is developed conventionally using a Maxwell pair, so defining the extent of the coil from its central plane toward one end. The return conductors for X and Y are folded back on themselves, so that both returns are on the same side of the coil central plane. This is effective in allowing excellent patient access to limited diameter coils but results in a very substantial torque on the coil assembly w h e n the gradients are pulsed, making it hard to anchor them and stop mechanical vibration of the whole structure. A solution is the use of additional "bucking" coils wound in series with the field generating windings and an opposing balancing torque [11]. This is illustrated in Fig. 5, which shows such a coil assembly. A general problem with insert coil systems arises because the gradient fields may terminate within the region of sensitivity of the RF coils used for transmission and reception. This may result in unwanted signals being aliased back into the desired image data. Care in the design of the RF coils and careful choice of slice selection arrangements can obviate these problems to a satisfactory extent.
CLINICAL RESULTS FROM DIFFUSION STUDIES The main initial clinical application of diffusionweighted imaging was in the study of stroke, where MAGMA (1994) 2(3)
changes in the apparent diffusion coefficient have been observed before any other indications on conventional MR images [12]. The significance of diffusionweighted imaging as an early indicator of acute injury is now also being explored in cases of perinatal hypoxic ischemic injury [13]. Reliable measurement of the apparent diffusion coefficient in vivo has proved to be difficult and has not added greatly to a clinical assessment of diffusionweighted images. This is largely because of problems with motion artifact, partial volume effects, and the markedly anisotropic properties of white matter of the brain, in particular, and in peripheral muscle tissue [14]. Figure 6 illustrates the appearance of diffusion anisotropy in vivo (in this case in a volunteer study).
THE APPEARANCE OF PERFUSION IN NORMAL IMAGING AND ITS APPLICATIONS Although perfusion and diffusion are often treated together as though they were synonyms for each other, their mechanisms and means of observation are very different. Because perfusion relates to the movement of blood through the microvasculature (venules) of parenchymal tissue, its observation is of significance in assessing the continuing viability of tissue. The study of perfused flow is currently of interest in connection with attempts to observe functional changes in the brain [15-17]. Signal changes associated with perfusion mediated variations in blood oxygenation states (the BOLD mechanism [18]) are attracting substantial attention at present. However, the ultimate efficacy of this model remains to be evaluated fully [19]. The use of bolus injections of Gd-DTPA to highlight changes due to perfusion is much more secure, although there is much work to be done to achieve the sort of quantitation performance that can be obtained with X-ray contrast agents. Work is however progressing on brain [20], heart [21], and kidney [22] using this approach. The impact of perfusion changes is destined to play an increasing role in MRI as interventional procedures involving any sort of hyperthermia are studied more extensively. The body's thermoregulatory mechanism responds, with some degree of lag, to thermal stresses that persist for more than a short time. The ensuing changes in perfusion can compromise measurements of temperature through the observation of tissue parameters [23]. Because of the problems found with the measurement of Tt (in particular as outlined in Ref. 23), the approach suggested by Le Bihan et al. [24]
Fig. 6. Pair of sagittal images of a normal adult volunteer to illustrate the appearance of anisotropically restricted diffusion. In both cases the images were acquired at 1 T, with TR = 1500 ms (determined by cardiac gating), TE = 130 ms and b was 550 s mm -2. (a) Sensitization in the L-R direction (perpendicular to the plane of the image). Note
the loss of signal in the corpus callosum and parts of the ports. Fibers running head to foot in the pons are clearly seen against a low-signal background. (b) Sensitization in the A-P direction. The corpus callosum now has high signal and the ascending/descending tracts no longer stand out in the anterior of the pons.
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using the diffusion coefficient m a y be better, even if more technically difficult [25]. Studies of both approaches are continuing in vivo [26, 27], with the hope that one or other m e t h o d will provide a satisfactory means of local tissue temperature measurement in vivo.
9.
10. 11.
CONCLUSION 12. The study of diffusion and per fusion in vivo is of increasing importance, a n d n e w applications are emerging for the quantitative investigation of both. It m a y take some time for these to become established, but t h e y are likely to be central to the study of the functional performance of the body.
13.
ACKNOWLEDGMENTS
14.
We are grateful to the Medical Research Council and Picker International Inc. for their continuing support and to our colleagues at the Robert Steiner MR Unit at Hammersmith Hospital. It is a pleasure to acknowledge the assistance of Dr. Martin King in performing calculations for the diffusion studies.
15.
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