Water Exchange

In the discussion above, and indeed in many studies employing dynamic contrast-enhanced MRI in oncology, it has been assumed that tissues contain a single, homogenous, water population with well described MR properties that undergoes simple changes when subjected to a contrast agent. However, experiments from the early days of biomedical MR suggested that the situation is more complex than this (Hazlewood et al. 1974). Water is found in a number of different environments in a biological tissue. The largest population is typically found inside cells. For example, water in the brain's grey matter may be coarsely divided into three populations: intracellular water making up around 79% of the total, interstitial water making up around 18% and intravascular water contributing the final 3%. Given the differing physiological environments of these spaces, it is not unreasonable to assume that the MR properties of water in the spaces will also be different (Hazlewood et al. 1974). As such it might be expected that T1 and T2 relaxation times (not to mention diffusion and magnetisation transfer coefficients) in the majority of tissues would have multiple components. This is seldom the case in practice, a finding that results from the rapid movement of water between tissue compartments, so called water exchange (Donahue et al. 1997). A water molecule moving from the cell, through the cell membrane and into the interstitial space during, for example, a T1 measurement will contribute a relaxation behaviour that represents an average of the intrinsic T1 of the cell and the intrinsic T1 of the interstitial space

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weighted by the time it spent in each of those spaces during the measurement. When many millions of water molecules contribute to the MR measurement a pattern or bulk property emerges. The more rapid the motion of the molecules and the smaller the difference between the relaxation times of the two spaces, the closer the relaxation pattern approaches a single average value (Donahue et al. 1994). At this limit, water exchange is said to be "fast". Conversely, as the motion of the water molecules slows down and the difference in relaxation times of the two spaces increases, the pattern of relaxation behaviour approaches that of two distinct populations. At the limit of no exchange between the two spaces during a relaxation measurement, water exchange is said to be "slow". Confusion with this nomenclature often arises since the terms fast and slow do not refer directly to the speed with which the water molecule moves between the two spaces, but to the ratio of this motion to the difference in relaxation rates of the two spaces (Barsky et al. 1997). Two spaces with identical relaxation rates will always be described as being in fast exchange however slowly the water molecules diffuse between them, as there can be no distinction made between their relaxation properties. Conversely, two spaces with orders of magnitude difference in their respective relaxation rates will remain in a slow exchange regime even if water moves very rapidly between them, as their relaxation properties will always be resolved. Moreover, a tissue said to have water undergoing fast exchange may switch to slow exchange without any modification to the speed at which the molecules move. This transformation may be initiated by a simple increase in the difference between the relaxation rates of the two compartments. For example, the addition of a contrast agent to the interstitial space does not change the motion of water molecules; it simply increases the intrinsic relaxation rate of the interstitial space.

The measurement of the tissue concentration of contrast agent is inextricably linked to the rate of water exchange between tissue compartments. Each of the approaches described in the chapter thus far assumes that water exchange is fast and that the tissue has a single, well defined, T1. In 1994, Donahue et al. performed a series of important experiments to determine the influence of water exchange on the measurement of contrast agent concentrations. They concluded that interstitial-intracellular water exchange was sufficiently rapid (between 8 and 27 Hz) that it was reasonable to assume fast exchange for clinical doses of contrast agent. These findings have been confirmed in a further study, like the Donahue study, performed on isolated perfused hearts (Judd et al. 1999). Nevertheless, both groups stressed the significance of contrast agent dose when considering the influence of water exchange. If the concentration of contrast agent in the interstitial space were to reach much higher levels, then the effects of slow exchange would be felt. These considerations have driven a series of studies by Landis et al. (1999, 2000) and Yankeelov et al. (2003) in which the interstitial-intracellular (transcy-tolemmal) water exchange process has been examined in detail. Indeed, Yankeelov et al. (2003) have introduced a methodology, BOLERO, for analysing contrast agent kinetics for systems departing the fast exchange limit. Central to their work is the suggestion that transcytolemmal water exchange departs the fast limit, in many tissues, at very low (sub-clinical) doses of contrast agent (Landis et al. 1999). This is at odds with the findings of Donahue et al. (1994) and Judd et al. (1999) and remains an area of continued debate. Critical to these studies is the accurate measurement of water residence times (average time that a water molecule resides in a compartment = 1/ exchange rate). Such measurements have been made over a number of years using contrast agents and diffusion measurements (Pirkle et al. 1979; PfeuffeR et al. 1998; Quirk et al. 2003), but no agreement has yet surfaced on the order of magnitude of these residence times.

Less controversial is the issue of intravascular-interstitial water exchange. Donahue et al. (1994) estimated exchange rates in the isolated perfused heart with an upper limit of 7 Hz while Judd et al. (1999) measured an intravascular-interstitial exchange rate of 3 Hz. Given the large difference in relaxation rates of the two spaces immediately following contrast agent administration (due to the fact that the agent will not have had time to pass into the interstitial spaces, whilst being present in high concentration in the intravascular space), these values explain earlier observations of significant departures from the fast exchange limit (Judd et al. 1995). This finding may have a serious practical implication for dynamic contrast-enhanced MRI studies in oncology, even though to date little data has been published on the issue of limited intravascular-interstitial water exchange and its affect on DCE-MRI. It is clear that experiments using intravascular contrast agents are much more sensitive to restricted exchange effects than those employing interstitial agents (Judd et al. 1999). For interstitial agents the degree of first pass extraction plays a major role in determining the magnitude of the effect. If contrast agent enters the interstitial space quickly then the effect of slow water exchange

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is short-lived. Larsson et al. described such effects in a study of perfusion of the heart and brain (Larsson et al. 2001). With an intact blood-brain barrier agents such as Gd-DTPA behave as intravascular contrast agent. As such, during the first pass of a bolus of Gd-DTPA through the brain intravascular-intersti-tial exchange approaches the slow limit (Larsson et al. 2001) and contrast agent concentrations (and thereby perfusion) are underestimated. On the other hand first pass extraction of Gd-DTPA in the heart is significant (> 30%) and the slow water exchange effect quickly decreases. In this case the early phase of contrast agent uptake is only underestimated very slightly (Larsson et al. 2001). With the assumption that first pass extraction is ~50%, not unreasonable for tumours, Larsson et al. (2001) conclude that water exchange will have minimal effect on the determination of ^trans for typical clinical doses of contrast agent. Further simulations of the signals obtained from the brain and brain tumours (Buckley 2002) support these findings. The initial peak seen in a signal-time plot during the first pass of a contrast agent bolus is flattened by the effect of slow intravas-cular-interstitial water exchange (Fig. 5.3). If the contrast agent remains intravascular (as seen in normal grey and white matter with an intact blood--brain barrier) this flattening will lead to underestimates in both perfusion and blood volume. Moreover, the mis

~ —, Fig. 5.3. Simulated signal-time curves for normal grey matter (grey lines) and white matter (black lines). The curves are representative of data obtained in a spoiled gradient echo acquisition (TR, 4.3 ms, flip 35°) when intravascular-interstitial water exchange is either in the fast limit (faint lines) or in the slow -,-, limit (bold lines)

match between the first pass peak and the subsequent equilibrium phase (in which the systems returns to the fast exchange regime) may be misinterpreted as contrast agent leakage (Buckley 2002). These effects are negated somewhat in tumour tissue where there is significant first-pass extraction of the contrast agent. However, estimates of blood volume and, to as lesser extent, separate estimates of perfusion and microvas-cular permeability-surface area product are compromised to some degree as their measurement depends upon very rapid data acquisition in the early phases of enhancement (Buckley 2002). At least two methods for controlling these effects have been proposed. Yankeelov et al. (2003) recommend an approach in which interstitial-intracellular water exchange is explicitly modelled and estimated. Though elegant in concept the additional burden of data analysis has certain limitations (Yankeelov et al. 2003), and these methods have not to date been applied in the consideration of intravascular-interstitial water exchange. Another approach, proposed by Donahue et al., is to minimise the exchange rate dependence of the measurements made. These exchange-minimisation techniques require the use of short inversion time magnetisation prepared sequences or short TR, high flip angle spoiled gradient echo acquisitions (Donahue et al. 1996). These imaging sequences suffer from the drawback of limited SNR, but they produce signals that are largely insensitive to changes or differences in water exchange effects. Finally, experimental design can play a significant role in the influence of water exchange on contrast agent measurements. Consideration must be given to the use of lower contrast agent doses, infusions rather than bolus injections or smaller, rapidly extracted, agents. These considerations will conflict with many other requirements for DCE-MRI acquisitions and a compromise must be reached for each given study.

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