Flow

Magnetic resonance imaging flow techniques allow the non-invasive observation of velocity profiles and hence residence times during aseptic processing and extrusion. MRI techniques useful in determining velocities and residence times fall under two broad categories: time-of-flight and velocity-encoded techniques (Listerud, 1991). Currently, time-of-flight techniques have seen more exposure in food science journals (McCarthy, et al., 1992a; McCarthy, et al., 1992b), and allow easier comprehension by non-physicists.

6.1. Time-of-Flight Techniques

Simply put, time-of-flight (TOF) methods mark or tag nuclei in a fixed volume at time zero and later interrogate the same or another volume to determine whether the nuclei have moved. TOF can characterize any pattern of motion, from flow in straight pipes (Caprihan and Fukushima, 1990; McCarthy, et al., 1992a) to complex heart muscle contractions (Zerhouni, et al., 1988; Axel and Dougherty, 1989) and radial motions in extruders (McCarthy, et al., 1992b). The method of tagging nuclei varies from simple slice selection to imposing a grid or a single black line. The TOF technique employing slice selection excites nuclei in a plane perpendicular to the direction of flow (tagged volume, Figure 7), pauses to allow development of the flow pattern, then interrogates the same volume or fluid volumes downstream from the initial slice. In the case of laminar flow, slices acquired from sequential volumes downstream will reveal concentric rings of intensity, corresponding to elements of the initial tagged fluid forming a paraboloid due to their increase in velocity with distance from the pipe wall. A three dimensional dataset representing the fate of a selected volume of fluid has thus been acquired. Another variation of TOF, patterned nulling of the intensity of a volume of fluid or tissue, allows observation of more complex motions by following the distortion of the selected pattern over time. Specific configurations of radiofrequency pulses in the presence of magnetic field gradients produce the desired motif of lines (see Extruder discussion). Imposing a pattern on a slice of fluid during pipe flow could also reveal radial or transverse mixing between layers, caused by turbulence.

6.2. Velocity-Encoding Techniques

The other MRI method for observing flow patterns involves movement of excited nuclei in a gradient, resulting in phase encoding of velocity. The basic technique resembles diffusion imaging, in that two gradients of opposite sign cancel spatial phase encoding of stationary nuclei; only nuclei which have moved during the encoding period accumulate phase in proportion to their displacement. Velocity-encoding differs from diffusion imaging in that while determination of a diffusion coefficient relies only on signal attenuation due to gradient-induced dephasing, velocity encoding actually quantifies phase differences by Fourier transformation of the cyclic pattern of intensity variation. The frequency of the cyclic variation, produced by the inversely coordinated incrementing of two field gradients from, e. g., negative through zero to positive, proves proportional to velocity. A two dimensional image designed in this way portrays spatial information on its frequency encode dimension, versus velocity along the phase encode dimension (Figure 8). The experiment can provide two dimensional positional information by including spatial phase encoding by a gradient orthogonal to the frequency encoding gradient, producing, in the case of laminar flow, a paraboloid similar to TOF datasets. The primary difference between the paraboloids lies in the flow dimension: TOF expresses the dimension as time; flow-encoding maps the third dimension as velocity. Both flow-encoding and time-offlight techniques can aid in the design and control of extrusion and aseptic processing.

Time-of-Flight Velocity Determination Centimeters from Tagged Volume

Figure 7. The most common time-of-flight velocity determination technique consists of selectively exciting (tagging) the nuclei within a plane (here 2 mm thick) perpendicular to the direction of flow. After allowing the flow pattern of the volume to develop, slices of fluid downstream from the tagged volume reveal intensity, and therefore velocity, dependent on radial position. Stacking the slices forms a paraboloid, the pattern of laminar flow.

Figure 7. The most common time-of-flight velocity determination technique consists of selectively exciting (tagging) the nuclei within a plane (here 2 mm thick) perpendicular to the direction of flow. After allowing the flow pattern of the volume to develop, slices of fluid downstream from the tagged volume reveal intensity, and therefore velocity, dependent on radial position. Stacking the slices forms a paraboloid, the pattern of laminar flow.

Vclocity-Encoded Laminar Plow

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