INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Data Analysis RESULTS DISCUSSION CONCLUSIONS REFERENCES

Pulsed magnetic field-gradients can be used in nuclear magnetic resonance (NMR) experiments to encode spatial information in spin-magnetization to measure positional displacement. The analogy of the resulting spatial coherences seen in NMR data to optical diffraction was first pointed out by Mansfield and Grannell (1973). Cory and Garroway (1990) showed that pulsed field-gradient spin-echo (PGSE) NMR diffusion measurements in heterogeneous systems can be used to obtain a displacement profile of molecules in a liquid, allowing the delineation of features of compartments too small to be observed using conventional NMR imaging. Callaghan et al. (1991) demonstrated interference-like effects in PGSE NMR diffusion studies of fluids in porous media and recently reviewed the spatial coherence phenomena arising from these experiments (Callaghan et al., 1999). We have conducted PGSE NMR diffusion studies of red blood cell (RBC) suspensions and showed that diffusion-diffraction and diffusion-interference of water occurs; this was used to show the alignment of RBC in the static magnetic field of the spectrometer and to estimate cell dimensions, detect shape changes with time, and to estimate membrane transport characteristics (Kuchel et al., 1997, 2000; Torres et al., 1998, 1999). It has been independently demonstrated that RBC align in a strong magnetic field with their disc planes parallel to the magnetic field (Higashi et al., 1993) so this was important in the design of the diffusion-simulation models used herein (see Materials and Methods).

Diffraction-like effects from PGSE NMR diffusion experiments can be visualized by plotting the relative signal intensities as a function of the spatial wave vector q, where q = (2)¹g, and where  is the magnetogyric ratio of the observed nucleus, g is the magnetic field gradient, and  is the duration of each of the magnetic field-gradient pulses used in the experiment. The resulting graph (q-space plot), from an RBC suspension consists of a series of maxima and minima whose positions in q space can be related to average cell dimensions and the average spacing of the extracellular cavities or "pores" (Torres et al., 1998, 1999). The positions of these features may also change when there is a change in the rate of exchange of diffusant across the cell membrane (Kuchel et al., 1997).

We have previously used simulations of diffusion in an RBC suspension, in the PGSE NMR context, to aid in the assignment of q-space features to particular modes of diffusion (Torres et al., 1999). Here we extend this work and demonstrate that these simulations provide further insights that are useful for the interpretation of q-space and diffusion tensor data from RBC suspensions. Specifically, we show that the q-space and diffusion tensor data contain information relating to the packing density of the cells in a suspension and the mean cell geometry. This study, therefore, extends the methodology and concepts used in interpreting data from PGSE NMR diffusion experiments on RBC suspensions and potentially in analogous cellular systems.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Data Analysis RESULTS DISCUSSION CONCLUSIONS REFERENCES

Simulations

Individual computer models were developed to simulate diffusion in a suspension of biconcave discs (Program I), and to simulate diffusion in a suspension of oblate spheroids (Program II). (All programs described in this report may be obtained from DGR at d.regan{at}mmb.usyd.edu.au.) These models enable the simulation of diffusion during a standard PGSE NMR experiment (Kuchel et al., 1997; Torres et al., 1998) and produce an array of signal intensities corresponding to the respective field gradient strengths specified for a simulated experiment.

The programs use a Monte Carlo technique to simulate diffusion in a three-dimensional (3D) hexagonal lattice of "virtual" cells (see Fig. 1) as described previously (Lennon and Kuchel, 1994a,b; Torres et al., 1998). The uniform arrangement of virtual cells in a hexagonal lattice, having an order parameter of unity, is justified on the basis that real RBC align in the magnetic field, and that it was the intention to design a canonical pure system to form the basis of the interpretation of experimental q-space data (see Discussion).

View larger version (60K): [in this window] [in a new window]   FIGURE 1   Hexagonal lattice of virtual cells. The figure illustrates the arrangement of cells (shown here as biconcave discs) used in the simulations of diffusion in the 3D infinite tessellation. The latter was effectively generated by the application of periodic boundary conditions to a unit cell.

Simulations were performed for ensembles of up to 10⁸ noninteracting point molecules on a 64 processor SGI Origin 2400 supercomputer (APAC National Facility, Australian National Univ., Canberra, Australia). The intrinsic ensemble nature of the calculations allowed ensembles to be split into smaller "packets" of ~200,000 point-molecule trajectories, which could be distributed across multiple processors. In this way the parallel capability of the supercomputer was used. When the full complement of trajectories was completed, the results were summed and averaged.

The simulations were of diffusion in a 3D hexagonal lattice of cells having either biconcave disc (Fig. 2 A) or oblate spheroid (Fig. 2 B) geometry. The analysis was expedited by invoking a "unit cell," consisting of a regular hexagonal prism containing a cell, centered on the Cartesian origin, and applying periodic boundary conditions, thereby simulating an infinite tessellation. (In all simulations and experiments discussed in this report, a Cartesian coordinate system was used such that the z axis was aligned with the static magnetic field, B₀, of the NMR spectrometer.) A random number generator and a random binary-digit generator were used to determine a random starting position for the trajectory of each point molecule (Regan and Kuchel, 2000). The same random number and random binary-digit generators were used to test for membrane transition and to choose random jump directions, respectively.

View larger version (14K): [in this window] [in a new window]   FIGURE 2   Cell geometry. (A) Two-dimensional representation of a biconcave disc whose shape and dimensions are defined by the parameters b, d, and h approximating those of a human red blood cell. (B) Two-dimensional representation of an oblate spheroid whose shape is defined by the parameters a (the distance from the foci, f, to the center of the oblate spheroid) and (not shown) whose values are calculated as a function of the x-, y-, and z-semi-axis values using Eq. 2 and Eq. 3. Rotation around the axis indicated by the dotted line generates the 3D cell shapes used in the simulations.

The biconcave disc in Program I was represented by a degree-4 equation in Cartesian coordinates (Kuchel and Fackerell, 1999). The shape of the biconcave disc (Fig. 2 A) was defined by the three parameters: b, thickness in the dimpled region; h, maximum thickness; and d, main diameter, whose respective values of 1.0 × 10⁶ m, 2.12 × 10⁶ m, and 8.0 × 10⁶ m were assigned to closely approach the shape of human RBC and to yield the known mean volume of human RBC of 8.6 × 10¹⁷ m³ (Dacie and Lewis, 1975). The points of intersection of point-molecule trajectories with the biconcave disc were calculated using a Newton-Raphson algorithm (Regan and Kuchel, 2000).

The oblate spheroid used in Program II is described by the function

(1)

where, a is the distance of the foci from the center of the oblate spheroid (Fig. 2 B), and the oblate spheroidal coordinate  is a constant (Moon and Spencer, 1988). The values of a and  were calculated, as functions of the specified values for the oblate spheroid semi-axes, using the formulae

(2)

(3)

where x, y, and z are the values of the oblate spheroid semi-axes (Fig. 2 B) for the body centered at the origin of a Cartesian coordinate system. The x, y, and z semi-axes were assigned values of 8.0 × 10⁶ m, 2.0 × 10⁶ m, and 8.0 × 10⁶ m, respectively. These values were chosen to match the overall dimensions of the biconcave disc but yielded a smaller volume of 6.7 × 10¹⁷ m³.

Another characteristic of a virtual cell that is useful for interpreting PGSE NMR data is the mean barrier separation in the cell. This value was calculated for both cell types in the x, z, and y directions. The calculation was performed by assigning a random coordinate inside the cell and calculating the length of the chord, in the relevant direction (x, z, or y), that intersected this point. This process was repeated for 10⁷ random coordinates and the average chord length calculated. The mean barrier separation in the x, z, and y directions for the biconcave disc and the oblate spheroid were 5.8 × 10⁶ m, 5.8 × 10⁶ m, and 1.8 × 10⁶ m, and 6.0 × 10⁶ m, 6.0 × 10⁶ m, and 1.5 × 10⁶ m, respectively.

For each cell type, the following simulations were performed: diffusant (water) confined by an impermeable membrane to the intracellular space; diffusant confined by an impermeable membrane to the extracellular space, and packing density or hematocrit (Ht, the volume fraction of the unit cell that is occupied by a cell) set to either 0.3, 0.4, or 0.5; and diffusant in both the intracellular and extracellular spaces and able to exchange through a semi-permeable membrane, with hematocrits (Ht) set to 0.3, 0.4, or 0.5.

Intracellular (D_in) and extracellular (D_out) diffusion coefficients were assigned values of 1.6 × 10⁹ m²s¹ and 8.0 × 10¹⁰ m²s¹, respectively, in accordance with preliminary estimates we have obtained experimentally (using standard PGSE NMR methods) for water in human RBC suspensions. The length of a jump, s, was calculated using the Einstein diffusion equation (Tanford, 1961),

(4)

where D is the diffusion coefficient in the relevant compartment (i.e., D_in or D_out), and t is the duration of a single jump (as determined from the assignment of other simulation parameters). For simulations in which the membrane was semi-permeable, the permeability (P_d) was assigned a value of 6.1 × 10⁵ m s¹ as has been determined experimentally for human RBC (Benga et al., 1990). For simulations in which the membrane was required to be impermeable, P_d was set to zero.

We have previously demonstrated that the probability of transition across the membrane (tp) when the membrane is intersected by a point-molecule trajectory, in the context of the simulations described here, is related to s (jump length) and P_d by (Regan and Kuchel, 2000)

(5)

The value of tp, therefore, depends on whether transition across the membrane is from the intra- or extracellular space.

The parameter values for the simulations were chosen to be identical to those used for the PGSE NMR experiments on RBC suspensions described in the Results. The PGSE NMR parameters for all simulations were as follows: field-gradient pulse duration,  = 2 ms; time interval separating field-gradient pulses,  = 20 ms; the magnitude of the field-gradient, g, was sequentially incremented in 96 steps from 0.0 to 9.9 T m¹; proton magnetogyric ratio,  = 2.675 × 10⁸ radian T¹. The phase shifts accumulated during the total diffusion time ( + ) for all point-molecule trajectories were summed and averaged, and the signal intensity calculated for each value of g.

It has been shown that magnetic susceptibility differences between the interior and exterior of oxygenated or carbonmonoxygenated RBC in a suspension are negligible (Endre et al., 1984). Hence the model did not incorporate differences in PGSE signal intensity that might ordinarily be expected to occur in a system that is heterogeneous in magnetic susceptibility and hence magnetic field.

PGSE NMR experiments

PGSE NMR diffusion experiments were conducted on RBC suspensions having HT values of 0.2, 0.3, 0.4, 0.5, and 0.6. The general methods (pulse sequences, etc.) used for conducting these experiments and for preparing RBC suspensions were as described previously (Kuchel et al., 1997; Torres et al., 1998, 1999).

The experiments were conducted at 298 K on a Bruker AMX400 spectrometer (Karlsruhe, Germany) with an Oxford Instruments 9.4 T vertical wide-bore magnet (Oxford, UK), using a Bruker 10 T m¹, z-axis gradient-diffusion probe. Identical pulse-sequence parameters were used for all experiments as follows: field-gradient pulse duration,  = 2 ms; time interval separating gradient pulses,  = 20 ms; 32 transients per spectrum. The magnitude of the field-gradient was incremented from 0.001 to 9.9 T m¹ in 32 equal steps. (Unless the first spectrum [corresponding to the smallest field gradient] was acquired with a small nonzero gradient, its phase was substantially different from the rest in the series; therefore a value close to zero (0.01 T m¹) was used.) The gradients were calibrated using the known diffusion coefficient of water in an isotropic and unbounded region (Mills, 1973).

The signal intensity was measured as the integral of the water resonance after automatic phase and baseline correction. Signal intensities were normalized with respect to that of the first spectrum before q-space analysis (see Data Analysis).

	Data Analysis

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Data Analysis RESULTS DISCUSSION CONCLUSIONS REFERENCES

q-Space analysis

Diffusion tensor calculations

Fourier transform analysis

(6)

Error analysis

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Data Analysis RESULTS DISCUSSION CONCLUSIONS REFERENCES

General

5

1

Simulations: exchange off

Intracellular diffusion

1

View larger version (15K): [in this window] [in a new window]   FIGURE 3   Simulation of diffusion in the intracellular spaces. q-Space plots derived from simulations of water diffusion inside biconcave discs (solid line) and oblate spheroids (dashed line). Point molecules were confined to the intracellular space by starting all trajectories inside the cell and setting Pd to zero.

Extracellular diffusion

1

View larger version (17K): [in this window] [in a new window]   FIGURE 4   Simulation of diffusion in the extracellular spaces. q-Space plots derived from simulations of water diffusion in the extracellular region measured in the z direction in (A) a lattice of oblate spheroids, and (B) a lattice of biconcave discs. The main graphs were plotted on a semi-logarithmic scale and were discontinuous in the regions containing (minutely) negative signal intensities. The insets were plotted on normal axes to show that the data were continuous over the entire range of q. The simulations were performed using a range of packing densities: Ht = 0.3 (solid line); Ht = 0.4 (dashed line); and Ht = 0.5 (dotted line). Molecules studied were confined to the extracellular space by starting all trajectories outside the cell and setting Pd to zero.

Simulations: exchange on

The results of simulations in which water was diffusing in both the intra- and extracellular regions and exchanging across the membrane are shown in Fig. 5. Signal intensities at given q values became larger as Ht was increased, and the pore-hopping shoulder (in the region of q = 0.75 × 10⁵ m¹) shifted to higher q values and became less pronounced.

View larger version (15K): [in this window] [in a new window]   FIGURE 5   Simulations of diffusion in both the intra- and extracellular regions in (A) a lattice of oblate spheroids, and (B) a lattice of biconcave discs. The q-space plots were derived using measurements of diffusion of water in the z direction, and the exchange across the membrane occurred at a rate that was determined by Pd = 6.1 × 105 m s1. The simulations were performed using a range of packing densities: Ht = 0.3 (solid line); Ht = 0.4 (dashed line); and Ht = 0.5 (dotted line).

q-Space plots for the two cell types when the diffusion was measured in the x, y, and z directions are compared in Fig. 6. Points to note are: 1) the overall increase in signal attenuation at given q values for the oblate spheroid relative to the biconcave disc; 2) a shift in the positions of coherence maxima to higher q values for the oblate spheroid; 3) a much lesser degree of signal attenuation, for a given q value, in the y direction than in the x and z directions for both cell types; and 4) the appearance of some additional critical points (Fig. 6 A, q = 2.3 × 10⁵ m¹ and 4.2 × 10⁵ m¹, and relative to Fig. 6 C) in the plots for the x direction, which were otherwise very similar to those for the z direction for both cell types.

View larger version (12K): [in this window] [in a new window]   FIGURE 6   Simulated q-space plots derived for water diffusion in suspensions of biconcave discs (solid lines) and oblate spheroids (dashed lines) measured in (A) the x direction, (B) the y direction, and (C) the z direction. The transmembrane exchange rate was determined by Pd = 6.1 × 105 m s1 and Ht was 0.5.

The apparent diffusion coefficients estimated from the diffusion tensor analysis (Table 1) decreased with increasing Ht. In the x and z directions, D_app values were virtually identical for both cell types but were larger for the biconcave disc in the y direction. In contrast, RMSD values (Table 2) were higher for the oblate spheroid than for the biconcave disc at equivalent Ht values. However, the same trend of decreasing RMSD with increasing Ht was observed for both cell types. Although no clear trend was evident in the positions of the first two diffraction minima (q_1,min and q_2,min) for either cell type, the positions of the pore-hopping shoulder (q_1,max) corresponded to smaller dynamic displacements as Ht was increased and the respective values were smaller for the biconcave disc than for the oblate spheroid.

PGSE NMR experiments

The q-space plots of the PGSE NMR data obtained from real RBC suspensions are shown in Fig. 7. These plots illustrate two very clear results: signal intensities decreased at a given q value with decreasing Ht, and the point of inflection discernible at q = ~1.0 × 10⁵ m¹ was more pronounced at lower Ht.

View larger version (17K): [in this window] [in a new window]   FIGURE 7   Experimental q-space data from PGSE NMR experiments on RBC suspensions having Ht = 0.2 (square), 0.3 (circle), 0.4 (triangle), 0.5 (inverted triangle), and 0.6 (diamond). Features of particular interest are q1,max at ~1 × 105 m1 and q1,min at ~1.75 × 105 m1.

Note that the high-power diffusion probe used in these experiments only allowed for the application of the magnetic field gradient coaxially with the static field (i.e., in the z direction). This limitation precluded the calculation of a diffusion tensor because this requires the gradient to be applied in at least six directions. In addition, the gradient values used in the experiment were restricted to a range over which it was possible to obtain sufficient signal-to-noise. Although it was possible to observe higher-order coherences with higher gradients, estimation of displacements from the data became increasingly error prone.

Fourier transform analysis of these data (Table 2) clearly showed that as Ht was increased the values of RMSD decreased. The relationship between RMSD and Ht was remarkably linear as evidenced by linear regression onto the data, which yielded the expression RMSD = (1.70 ± 0.02) × 10⁷  ((1.20 ± 0.05) × Ht), with a correlation coefficient of 0.99. However, dynamic displacements calculated from q-space data were difficult to determine using the analytical methods that have been developed so far, and no clear trends were apparent in the values estimated. Although the dynamic displacements corresponding to q_1,min, q_1,max, and q_2,max were smaller than the corresponding values for the simulated data from biconcave discs and oblate spheroids, they were of comparable magnitude.

	DISCUSSION

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Simulations: exchange off

We have considered two cases of simulation in which exchange across the membrane was prevented by setting P_d to zero. The first case was where the diffusant (water) inside the cells alone was studied. The second case was where the diffusant in the extracellular region alone was studied. In the latter case, simulations were conducted at three Ht values, 0.3, 0.4, and 0.5.

Intracellular diffusion

6

Extracellular diffusion

Simulations: exchange on

The simulations of diffusion involved identical systems to those described in the section above, but they were conducted with exchange occurring between the intra- and extracellular regions. Molecules were assigned initial coordinates either inside or outside the virtual cell in a random manner, with a distribution (inside or outside) that was determined by the Ht. One measure of the robustness, or reproducibility, of these simulations was that, at a given Ht, the final distribution of point molecules between the intra- and extracellular spaces did not change to a statistically significant extent from the initial distribution.

Relative to the simulations of diffusion in which exchange was absent, decreasing the Ht resulted in a greater degree of signal attenuation with increasing q value (Fig. 5). Again, this is attributable to the diffusant in the extracellular region being less restricted as the spacing between the cells was increased. This observation is reinforced by the estimates of the D_app and RMSD values, which, without exception, increased with decreasing Ht (Tables 1 and 2). It is also notable that the pore-hopping shoulder was more pronounced at lower Ht values as a result of the proportionally increased contribution to the signal from the extracellular water. The additional critical points observed in Fig. 6 A arise from the fundamentally different topological arrangement of pores and cells in a hexagonal array when projected in the x and z directions.

The data in Table 2 show that RMSD values were slightly smaller for the biconcave disc than for the oblate spheroid. This result is opposite from that obtained for either intra- or extracellular diffusion in the absence of exchange. Thus the estimate of the apparent diffusion coefficient (directly related to the RMSD) in a two-compartment system with exchange is a nonlinear weighted sum of the apparent values in each compartment.

PGSE NMR experiments

The simulations described above were conducted to improve our interpretation of data obtained from PGSE NMR experiments on real cellular systems. It was shown that the biconcave disc simulations did indeed give rise to features that were seen in q-space plots from RBC suspensions.

However, as seen from (Fig. 7) and previous reports (Benga et al., 2000; Kuchel et al., 1997; Torres et al., 1998, 1999), the various features and critical points of the q-space plots were less pronounced than for the simulated canonical data. This is readily interpreted as being due to real RBC suspensions having a distribution of cell sizes and, to a lesser extent, shapes. In addition, the cells in a real suspension in the NMR spectrometer, although virtually completely aligned in the z direction, will not be so aligned in the x and y directions. Also, they move slightly during each NMR pulse sequence and therefore will be arranged in a continuously changing and random manner. The simulations were conducted on systems in which all cells were identical both in size and shape, and their orientations were exactly specified with their packing arrangement fixed and regular. Further work could entail building in random fluctuations in cell orientation and this would lead to a blurring of the features of q-space plots.

It is also clear from the experimental data (Fig. 7) that the extent of signal attenuation was increased at all values of q as Ht was decreased, as occurred with the simulated data. The pore-hopping shoulder was more pronounced at lower values of Ht, and this is attributed to the greater volume of water in the extracellular region resulting in its greater contribution to the overall water signal. However, had the Ht been further decreased, it is anticipated that, at some value, this feature would have become less pronounced and eventually disappeared altogether as the extracellular pores would have become ill-defined.

Also in Fig. 7, a decrease in Ht was accompanied by an increase in RMSD, reflecting the diminished restriction to diffusion in the extracellular region afforded by the lower volume occupied by the RBC. Once again, this result was observed in the simulations. The relationship between Ht and RMSD was very linear (see Results), thus suggesting a method for estimating the Ht of a sample simply by measuring the width-at-half-height of the Fourier transform of the q-space plot. The RMSD at Ht = 0.5 was considerably higher than that for the biconcave discs at the same Ht, and was closer to that for the oblate spheroids. The reason for the discrepancy lies in the values chosen for the intra- and extracellular diffusion coefficients for which only preliminary experimental values were used in the simulations.

The features of the q-space plots in Fig. 7 are not highly resolved, and, consequently, determination of the critical q-values was more difficult than for the simulated data. Nevertheless, the relationships between critical values and characteristics of the cells in the suspension at Ht = 0.5 are comparable with the simulated data at Ht = 0.5.

General points

It has been pointed out above that, in a real RBC suspension, the cells are not of identical size and are not motionless in a regular lattice. The models used in this study, in contrast, were based on an ideal and hence simplified system. The intention in the work was not merely to provide a simplification but rather to develop a canonical system that would reveal features that would be difficult to discern in a more realistic system due to the blurring effect of randomization of cell orientation.

The degree of signal attenuation in the PGSE NMR experiments on real RBC suspensions extended to greater than 10³. Despite this high level of attenuation, we are able to ignore the contaminating signals from other cellular metabolites or components. The concentration of water protons in the cell is 70-80 M and close to 100 M in the extracellular fluid. The concentration of nonexchangeable glycyl protons from glutathione, the most abundant metabolite inside the cells, is just 4 mM, a factor of 10⁵ lower than water. The hemoglobin concentration, although significantly higher, has a short T₂ relaxation time, so, in PGSE NMR experiments with an echo time of greater than 20 ms, the hemoglobin makes no significant contribution to the signal in the region of the water resonance (Kuchel and Chapman, 1991).

A complicating factor in the analysis of simulation data has been the appearance of negative signal values at the minima. The magnitude of these negative echoes was, on average, of the order of 10⁵ of the initial signal intensity. Although methods have been developed to overcome this difficulty (see Materials and Methods), considerable thought was given to the origin of this phenomenon. At the much less than Avogadro's number of trajectories performed for any single simulation, there will always be an excess of displacements in the ensemble in either the positive or negative direction along any axis. Any excess, however small, will constitute a degree of apparent flow and will give rise to negative spin-echo signal intensities (Callaghan et al., 1999).

q-Space data from real or simulated cell suspensions is clearly not Gaussian, and, consequently, the propagator obtained from the Fourier transform of the data is also not Gaussian. However, fitting a Gaussian to a typical q-space data set yielded a width-at-half-height of (2.27 ± 0.01) × 10⁴ m with a correlation coefficient of 0.99. Therefore, on the basis that the propagator is approximately Gaussian, we contend that the width-at-half-height of the Fourier transform of q-space data is related to the effective RMSD (see Eq. 6).

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Data Analysis RESULTS DISCUSSION CONCLUSIONS REFERENCES

We used random walk simulations of diffusion to study the relationship between the features of NMR q-space data and the shapes of the cells in the sample. Different cell geometries gave rise to differences in features in the q-space plots, so this finding will be useful in detecting pathological changes in cells and in the identification of cell types (Torres et al., 1998). We have pointed out the differences that exist between the simulated and real-cell suspensions. The ideality of the simulated systems has, in fact, allowed us to identify features in q-space plots that appear with lower resolution in such plots from real RBC suspensions. Thus, we could assign these features of q-space plots to particular modes of diffusion in an ideal setting. Two methods for facilitating the analysis were described: first- and second-derivative analysis of q-space plots for the determination of q values of critical points in q-space plots, and Fourier transform analysis for calculating apparent RMSD values. The latter method provides a quick and simple means of determining the Ht of cell suspensions. Finally, we used diffusion tensor analysis to estimate the apparent diffusion coefficients and to show their dependence on direction of movement of the diffusant in a heterogeneous system, such as a suspension of cells with only one axis of symmetry.