New Insights into Tumor Microstructure Using Temporal Diffusion Spectroscopy

Magnetic resonance imaging (MRI) can be adapted to provide noninvasive measurements of water mobility in biological tissues, and diffusion-weighted MRI has been widely adopted for clinical and research applications. The rate of water diffusion within tissues measured by conventional MR methods is found to be significantly lower than for free solutions, and measurements are often summarized in terms of an apparent diffusion coefficient (ADC), which is a measure of the effective distance over which water can migrate within tissue within a specified time. The ADC differs from the intrinsic diffusion coefficient D₀ in a manner that is dependent on the microstructure and composition of the tissue. A number of pathologic conditions, such as ischemic stroke (1, 2) and prolonged seizures (3, 4), produce significant changes in the ADC compared with healthy tissues. The ADCs of several tumors have been shown to be significantly different from those of surrounding healthy tissues, a finding that has led to interest in using diffusion-sensitive MRI not only as a diagnostic tool but also to assess tumor cellularity and changes in ADC that may reflect the response to treatments (5, 6).

The increasing use of diffusion MRI in clinical oncology has highlighted the need for a more quantitative understanding of the pathophysiologic factors affecting water diffusion rates in tissues. The rate of water diffusion in tissues is reduced whenever there are physical obstructions or hindrances to free Brownian motion and free exchange between different compartments, giving increase to restricted diffusion. Currently used measuring techniques are sensitive to the integrated effects of restrictions on water displacements at all spatial scales up to the order of several micrometers. The specific contributions of interactions with subcellular structures and macromolecules that occur on much smaller scales cannot then be distinguished from effects at larger dimensions. In particular, although it is well-documented that an increase in tumor cellularity is marked by a decrease in ADC, and that an increase in ADC is often indicative of positive treatment response (7–14), the roles that changes at the subcellular level play in affecting such measurements are not clear. Changes in membrane permeabilities, the relative sizes of various intracellular and extracellular water fractions, active transport mechanisms, and the precise nature of intracellular structures and their organization, may all have significant influences on the aggregate ADC of tissue (15–18). Because conventional measurements are unable to distinguish restrictions to diffusion that occur on scales smaller than several micrometers, we have explored a modified imaging technique that can selectively examine water mobility over much shorter spatial scales, much less than the diameter of a single cell. In this article, we report how information may be gleaned about structural changes that occur on a subcellular scale rather than merely reflecting cell density.

A more complete description of the physics of diffusion MRI may be found elsewhere (19–21), but here, we briefly illustrate the conceptual difference between our method and currently used techniques. Figure 1 depicts the pulsed gradient spin-echo (PGSE) pulse sequence, the most commonly used method for measurements of ADC with MRI. The significant feature of this sequence is that it uses a pair of diffusion-sensitizing magnetic field gradients, each of equal time length δ and magnitude G_D, separated by a time Δ, the “diffusion interval.” The initial gradient pulse serves to label the phase of the transverse magnetization from water molecules spatially along the applied gradient direction, and the subsequent pulse exactly reverses this phase if they do not move. Water molecules that undergo displacements along that particular direction in the diffusion time Δ will retain a net phase shift, and the mixing of different phases from random movements within the sample causes the net signal to be reduced. Thus, the MR signal is attenuated to a degree that depends on the variance of the displacements of water molecules during the interval Δ and the gradient G_D. A more quantitative description of this attenuation is presented in the Materials and Methods section.

A practical consideration for making measurements of diffusion is the gradient strength available to induce significant signal attenuation. As shown below, the interval Δ must be increased to achieve reasonable reductions in signal strength when the gradients are weak. Given the practical limits on the strengths of gradients available on current scanners, this interval is usually at least on the order of tens of milliseconds and is often set to several tens of milliseconds to achieve bigger effects (22–30). The Einstein equation relates the mean molecular displacement due to diffusion D over a time Δ: for a one-dimensional random walk along the direction of the gradient, the mean square displacement of the water molecules is,

For example, a molecule diffusing at the rate of 2.5 μm²/ms (≈D₀ for free water at 37°C) for an interval of 35 ms should on average undergo a net displacement of just >13 μm, a distance comparable with the diameter of a typical cell. If water molecules encounter a restrictive barrier to diffusion on or below this scale, 〈L〉 will be smaller and the diffusion rate (ADC) will seem to be lower. But if restrictions also occur on even smaller scales, these effects will not be distinct at this diffusion interval. No information can be obtained about effects below the scale of 〈L〉. To overcome this limitation, we have implemented an oscillating gradient spin-echo (OGSE) technique to be able to probe tumor microstructure at smaller dimensions. In this method, the pulsed gradients of the PGSE technique are replaced with sinusoidally varying gradients of frequency f (Fig. 1B). This approach reduces the effective diffusion interval below the period of one oscillation, yet the achieved signal attenuation is still significant (see Materials and Methods). By oscillating gradients at several hundred Hertz (Hz), effective diffusion times approaching one millisecond may be achieved, allowing spatial displacements nearly an order of magnitude smaller than those obtainable with current PGSE techniques to be probed (31, 32). Furthermore, by varying the frequency f, it is possible to characterize the various scales over which restrictions to diffusion occur in a complex system.

In this study, we have applied OGSE methods to map the ADC in rats bearing glioblastoma tumors in vivo and ex vivo to illustrate the increased contrast and structural information that is achievable using such techniques. By demonstrating an increased contrast in calculated ADC maps, as well as quantitatively different ADCs measured in pathologic regions, we show the potential benefit of OGSE techniques over currently used techniques for evaluating microscopic variations in tumor microstructure.

Animal model. All procedures were approved by our Institution's Animal Care and Usage Committee. Ten male Wistar rats (∼250 grams) were immobilized and anesthetized with a 2%/98% isoflurane/oxygen mixture. The rats were inoculated with 1 × 10⁵ C6 glioblastoma cells using a 10-mL gastight syringe ∼1 mm anterior and 2 mm lateral to the bregma on the right side of the head, at a depth of 3 millimeters relative to the dural surface. The C6 is a common brain tumor model that is widely used in experimental neuro-oncology to evaluate tumor growth, invasion, migration, and blood-brain barrier disruptions, and has been used extensively to investigate the efficacy of various therapies including chemotherapy and radiation therapy (33). Complete and acceptable data were obtained from only seven rats.

In vivo imaging. Fourteen days after tumor inoculation, MRI studies were performed on a Varian 4.7T horizontal bore imaging system. Anesthesia was induced and maintained with a 2%/98% isoflurane/oxygen mixture, and a constant body temperature of 37°C was maintained using heated air flow. Animals were placed in a prone position and imaged using a quadrature 63-mm inner diameter radiofrequency (RF) coil.

A multislice gradient echo imaging sequence [repitition time (TR) =150 ms; echo time (TE) = 3.5 ms; 128 × 128 matrix; 36 × 36 mm² FOV; 2-mm slice thickness] was used to acquire seven slices for proper positioning and slice selection. A subsequent T₂-weighted, single-slice fast spin-echo scan with 8 echoes (TR = 2,000; 13 ms echo spacing; 128 × 128 matrix; 36 × 36 mm² FOV; 2-mm slice thickness) was used for anatomic clarification of the tumor region. The same slice was then imaged using our OGSE technique, with oscillation frequencies ranging from 30 to 240 Hz, in 30 Hz increments. Diffusion-weighted scans were respiratory gated, with TR/TE = 2,000/76 ms, 64 × 64 matrix size, 2-mm slice thickness, and 36 × 36 mm² FOV. Two acquisitions were averaged for each image, each with b values of 0 and 401 s/mm². Each gradient pulse was 33.33 ms duration, so that the number of cycles varied from 1 to 8 and the gradient amplitude varied from 4.77 to 36.0 gauss/cm. After the OGSE imaging, conventional PGSE images were obtained with δ = 3 ms, Δ = 15 ms, and the diffusion sensitizing gradient set to 12.18 gauss/cm to obtain a b value of 401 s/mm², equal to that in the OGSE scans. Also, all PGSE scans were collected twice, each with opposite gradient polarity, and averaged to eliminate the presence of gradient crossterms that may influence ADC measurements (34). These crossterms are absent in our version of OGSE images. All other imaging variables were identical to the OGSE acquisitions. Diffusion gradients were placed simultaneously along all three imaging coordinate axes to obtain the maximum diffusion weighting with the available gradient amplitudes.

In addition, a single animal was imaged at higher resolution to more finely probe intratumor heterogeneity and facilitate comparison to ex vivo images acquired after perfusion fixation of the brain with formalin. For this animal, both PGSE and OGSE images were collected in vivo using a single 1-mm axial slice, with TR/TE = 2,000/76 ms, 128 × 128 matrix, 36 × 36 mm² FOV, with number of excitations (NEX) = 6. Only the 240 Hz OGSE data were collected.

Perfusion fixation. Four days after the imaging experiment, the rat was anesthetized, and then anticoagulated with 80 mg/kg pentobarbital i.p., with 0.01 mL/100 grams heparin added to the syringe. Once deep anesthesia was accomplished, surgery was performed to allow a blunt 16-gauge perfusion needle to be inserted into the left cardiac ventricle toward the left ventricular outflow tract, and just into the aorta. A saline wash solution was then perfused, with the right atrial appendage cut immediately to allow the rapid outflow of blood and wash solution. At this time, the perfusate was switched to 10% formalin in 0.1 mol/L phosphate buffer. Fixation began at a high flow rate (50 cc/min) for 2 to 5 min, then continued at a slow drip for 12 to 15 min until adequate fixation was achieved. The whole-brain tissue was then dissected and placed in fixative solution. Approximately 24 h later, the fixative was removed and the brain was placed in PBS (1×) for imaging.

Ex vivo imaging. Ex vivo images were performed on a single axial slice with TR/TE = 2,000/76, 96 × 96 matrix, 18 × 18 mm² FOV, 1-mm slice thickness, and NEX = 60. As with the in vivo data, all PGSE diffusion variables were kept the same (including reversed polarity of the gradient amplitudes), and only the 240 Hz OGSE data were obtained. Although we cannot be certain that the single imaging slice acquired in the ex vivo experiment was exactly the same as that recorded in vivo, several multislice scout images were used to choose the slice that most closely resembled the in vivo data.

Calculation of ADC maps. Using the formalism of Stejskal and Tanner (19), the diffusion attenuated signal magnitude, S, is related to the unweighted signal, S₀, such that:

where b represents the diffusion weighting imparted upon the sample by the time-dependent magnetic field gradients G_D(t) and is equal to:

where γ is the gyromagnetic ratio of hydrogen protons, and is equal to 42.58 Mhz/Tesla. Integration of this equation for the pulsed-gradient spin-echo experiment yields:

whereas the integration for the cosine-modulated gradients used in this study yields:

where N is the number of gradient oscillations per diffusion weighting duration T. The period, P, of one oscillation is equal to

where f is the frequency of oscillation (in Hz). The effective diffusion time for the oscillating gradient waveform is then

For a more complete description of these calculations, see ref. 32. Note that the effective diffusion time in OGSE depends on the oscillation period only and is no longer related to the time between gradient pulses.

All data were analyzed using Matlab 2007a (The Mathworks). Diffusion weighted images were registered to nondiffusion weighted (b = 0) images using a rigid registration algorithm. Regions of interest in subcortical gray matter, tumor, and whole brain were manually drawn and segmented with reference to high resolution anatomic images.

Figure 2 shows the maps of ADC, calculated using Eq. 2 above, obtained in one representative animal for different gradient frequencies. The ADC map obtained at the lowest frequency, 30 Hz, is similar to that obtained by the PGSE method, as expected. However, as the oscillation frequency is increased, there is increased contrast between the tumor and surrounding tissues, and new features appear within the heterogeneous tumor volume. These features correspond to regions in which the degree of restriction to diffusion varies more at shorter time and distance scales than at longer times.

Plots of ADC versus oscillation frequency for two regions of interest (within tumor and normal brain) from one representative animal are shown in Fig. 3. For each frequency, the corresponding mean displacement for free diffusion predicted by Eq. 1 is also displayed. At the lowest frequency of 30 Hz, the effective diffusion time is ∼8.3 ms (32), and the ADC is similar to that measured by PGSE methods over an interval of 15 ms. However, as the oscillation frequency increases, and the effective diffusion time decreases, there is a clear departure in ADC from that measured with PGSE methods. For example, at an oscillation frequency of 150 Hz (Δ_eff ≈ 1.7 ms), the ADC calculated using OGSE is ∼20% larger than that calculated using PGSE and becomes 48% larger at 240 Hz (Δ_eff ≈ 1.0 ms).

The ADC in contralateral gray matter was found, in general, to be smaller than that in tumor, and to increase less with frequency, with the mean value for gray matter varying from 0.60 ± 0.06 μm²/ms at 30 Hz to 0.79 ± 0.06 μm²/ms at 240 Hz (errors for values averaged across all animals are reported as SE). These values are consistent with previous reports of both human and animal brain (35–40). Although subcortical regions of the brain showed some increase in ADC with increasing frequency, this variation was less significant than that seen in tumor, indicating that in normal gray matter, restrictions occur on even smaller scales. These differences are likely due to the densely packed layers of nerve cell bodies (neurons and glial cells) comprising the cerebral cortex compared with the morphologically multiform structure of the C6 model. The C6 glioma model is known to exhibit intratumor regions of necrosis and hemorrage, as well as nuclear pleomorphism, resulting in a broader range of structural components in contrast to the finely packed, granular structure of the cerebral cortex (41).

Figure 4 presents a further analysis of the data shown in Fig. 2. For voxels within the tumor region of Fig. 2, the ADC obtained by the PGSE method was plotted against the values obtained by OGSE for three frequencies (30, 150, and 240 Hz). The ADCs obtained by OGSE methods are quantitatively larger than those acquired by PGSE methods, thus creating the larger contrast between tumor and healthy tissue as revealed in Fig. 2. The results for ADCs obtained by both methods in distilled water are also shown, with the expected clustering near the line of equality.

Figure 5 shows a histogram of the percentage difference between ADCs calculated using OGSE versus PGSE methods at the same three frequencies for voxels in both tumor and whole brain in the same animal. The percentage difference is defined as:

where ADC_PGSE and ADC_OGSE are ADC values measured via PGSE and OGSE, respectively. Shown in these plots are the results for tumor in one animal (A), as well as across all six animals (B), and for whole brain in one animal (C), and whole brain (D) across all six animals. The percentage differences are larger at higher frequencies in both tumor and whole brain.

To test the statistical significance of this departure, a paired Student's t test was performed. For each animal at each oscillation frequency, the mean ADCs obtained via PGSE and OGSE for all voxels within a manually drawn region of interest were compared. The means were statistically different (P < 0.05) at all frequencies above 120 Hz (and P < 0.01 at 150, 210, and 240 Hz).

An additional study was performed to examine the results at higher resolution in vivo, and ex vivo after perfusion and fixation. These results are shown in Fig. 6. Figure 6 depicts a single T₂-weighted axial slice in vivo showing the tumor in A and the resulting ADC maps measured using PGSE and OGSE methods in B and C, respectively. The mean ADC found in the whole tumor region of interest was 1.12 ± 0.07 μm²/ms using the OGSE method and 0.92 ± 0.07 μm²/ms for the PGSE method. For comparison, values in contralateral healthy subcortical gray matter were found to be 0.64 ± 0.09 μm²/ms (OGSE) and 0.54 ± 0.09 μm²/ms (PGSE).

Four days after imaging, the brain was fixed as described in the Materials and Methods and imaged ex vivo the following day. These results are also shown in Fig. 6, with the T₂-weighted image in D, the ADC map obtained using the PGSE method in E, and the ADC map obtained using the OGSE technique in F. In this case, the mean ADC in tumor was found to be 1.18 ± 0.06 μm²/ms using the OGSE method, and 0.52 ± 0.05 μm²/ms using the PGSE technique, compared with subcortical gray matter ADCs of 0.64 ± 0.09 μm²/ms (OGSE) and 0.38 ± 0.08 μm²/ms (PGSE). Not only does the OGSE method provide quantitatively different ADCs but also the corresponding ADC maps reveal more pronounced contrast in the tumor. Moreover, the OGSE data for both normal brain and tumor change less between the in vivo and ex vivo conditions, possibly because the PGSE data are dominated by changes in the sizes and tortuosities of intracellular and extracellular spaces.

Our measurements and analysis show there were statistically significant differences in ADC obtained by OGSE methods at moderate to high frequencies (equivalent to short diffusion intervals) compared with conventional PGSE methods, and these differences varied for different tissues. The broader range of ADC values at higher frequencies produces greater contrast in the corresponding parametric ADC maps and provides details within the tumor that would otherwise be obscured by conventional techniques. This may be of particular value for assessing the efficacy of therapeutic agents at their earliest stage and in a noninvasive manner. Although conventional imaging methods have been shown to be effective in assessing tumor cellularity and therapeutic response, their inability to identify changes in diffusion processes over intracellular spatial scales renders the information from these methods incomplete. It is reasonable to postulate that changes in the organization and integrity of intracellular spaces occur before cells undergo apoptosis or lysis. The ability to measure microscopic structural changes over previously unachievable spatial scales should therefore provide a more complete and potentially more sensitive assessment of tumor growth and response to treatment.

Using the OGSE technique, we have been able to assess water displacements over only a few micrometers within a tumor environment. It should be noted that our selection of a 15-ms diffusion time for comparative PGSE experiments was very modest compared with those typically used in a clinical setting. In the majority of clinical studies to date, investigators routinely measure over much longer diffusion times, corresponding to displacements of tens of micrometers or more (22–30). Our results indicate a significant benefit in measuring water displacement over much shorter times and, thus, spatial scales, as evident in the increased contrast of ADC maps.

It is widely accepted in the literature that the ADC within biological tissue is diminished from the intrinsic value of tissue water, D₀, due to the presence of barriers that restrict diffusion, such as nuclear and cellular membranes and intracellular organelles. However, although several studies have provided evidence of modest reductions in ADC at increasing diffusion times (42–45), we have shown a significant increase in ADC at decreasing diffusion times, before many of the larger scale barriers have been encountered. In several of the tumors, we were able to measure ADC values >50% of that of free water, and with the use of even higher gradient frequencies, can expect to push this toward the limiting true intrinsic value.

In principle, shorter diffusion times can be achieved using PGSE methods, but reducing the diffusion interval Δ to values of 1 ms or below while still maintaining a large b value would require extremely strong gradients and power supplies that are prohibitively expensive and cumbersome. For the OGSE method in preclinical studies, gradients of appropriate strength are readily available for small animal MRI scanners that can achieve high gradient oscillation frequencies >1 kHz, with effective diffusion times down to a fraction of a millisecond. At such frequencies, OGSE methods will be capable of examining tissue microstructure over spatial scales less than a single micrometer, when changes in intracellular structure and, for example, nuclear size should become apparent. We have previously reported similar measurements in globally ischemic rat brain (40). We believe these studies will further support the claim that OGSE measurements are not only a more precise indicator of variations in tissue microstructure, but that measurements of ADC over an appropriate range of spatial scales may predict treatment response earlier than those measurements over a single length scale.

No potential conflicts of interest were disclosed.

Grant support: NIH grants RO1CA109106, RO1NS034834, U24 CA 126588, and 1K25 EB005936.

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

We thank the NIH for financial support through grants RO1CA109106, RO1NS034834, U24 CA 126588, and 1K25 EB005936; Jarrod True for expert animal care assistance; and Richard Baheza for expert technical MRI assistance.