In vivo imaging of cancer cell size and cellularity using temporal diffusion spectroscopy.
Journal: 2017/July - Magnetic Resonance in Medicine
ISSN: 1522-2594
Abstract:
A temporal diffusion MRI spectroscopy based approach has been developed to quantify cancer cell size and density in vivo.
A novel imaging microstructural parameters using limited spectrally edited diffusion (IMPULSED) method selects a specific limited diffusion spectral window for an accurate quantification of cell sizes ranging from 10 to 20 μm in common solid tumors. In practice, it is achieved by a combination of a single long diffusion time pulsed gradient spin echo (PGSE) and three low-frequency oscillating gradient spin echo (OGSE) acquisitions. To validate our approach, hematoxylin and eosin staining and immunostaining of cell membranes, in concert with whole slide imaging, were used to visualize nuclei and cell boundaries, and hence, enabled accurate estimates of cell size and cellularity.
Based on a two compartment model (incorporating intra- and extracellular spaces), accurate estimates of cell sizes were obtained in vivo for three types of human colon cancers. The IMPULSED-derived apparent cellularities showed a stronger correlation (r = 0.81; P < 0.0001) with histology-derived cellularities than conventional ADCs (r = -0.69; P < 0.03).
The IMPULSED approach samples a specific region of temporal diffusion spectra with enhanced sensitivity to length scales of 10-20 μm, and enables measurements of cell sizes and cellularities in solid tumors in vivo. Magn Reson Med 78:156-164, 2017. © 2016 International Society for Magnetic Resonance in Medicine.
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Magn Reson Med 78(1): 156-164

<em>In vivo</em> imaging of cancer cell size and cellularity using temporal diffusion spectroscopy

Purpose

A temporal diffusion MRI spectroscopy based approach has been developed to quantify cancer cell size and density in vivo.

Methods

A novel Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion (IMPULSED) method selects a specific limited diffusion spectral window for an accurate quantification of cell sizes ranging from 10 to 20 μm in common solid tumors. In practice, it is achieved by a combination of a single long diffusion time pulsed gradient spin echo (PGSE) and three low-frequency oscillating gradient spin echo (OGSE) acquisitions. To validate our approach, H&amp;E staining and immunostaining of cell membranes, in concert with whole slide imaging, were used to visualize nuclei and cell boundaries, and hence enabled accurate estimates of cell size and cellularity.

Results

Based on a two compartment model (incorporating intra- and extracellular spaces), accurate estimates of cell sizes were obtained in vivo for three types of human colon cancers. The IMPULSED-derived apparent cellularities showed a stronger correlation (r=−0.81, p<0.0001) with histology-derived cellularities than conventional ADCs (r=−0.69, p<0.03).

Conclusion

The IMPULSED approach samples a specific region of temporal diffusion spectra with enhanced sensitivity to length scales of 10–20 μm, and enables measurements of cell sizes and cellularities in solid tumors in vivo.

Introduction

Diffusion-weighted MRI (DWI) provides a non-invasive way to map the diffusion properties of tissue water molecules that are affected by restrictions and hindrances to free movement, and is thereby able to provide information on tissue microstructure. Conventionally, an effective mean diffusion rate, the apparent diffusion coefficient (ADC), is obtained by using motion-sensitizing pulsed gradient spin echo (PGSE) pulse sequences to probe water displacements. Despite substantial successes in using ADC values for cancer diagnosis, staging, and assessment of response to treatment (1), the biophysical mechanisms underlying changes in ADCs are not always fully understood. ADC values are potentially affected by various tissue properties, including cellularity (2,3), cell size (4), nuclear size (5), membrane permeability (6), and the presence of necrosis (7), which are commonly involved in the development and treatment of cancer. Interpretation of changing ADC values must, therefore, be made with caution (8,9). Direct measurements of salient features of tissue microstructure at the cellular level could provide more valuable assessments of tumor development and therapeutic response than non-specific ADC values (9).

Cell size plays an important role in affecting the functional properties of cells from the molecular to the organismal level, including cellular metabolism (10), proliferation (11) and tissue growth (12). Monitoring changes in cell size is relevant to a wide array of clinical and research questions. For example, cell swelling is the first manifestation of various chemo/radio-therapy induced cell injuries (1,7). Also, cell shrinkage is a hallmark of morphologic features associated with apoptosis, which is a common target for many anti-cancer therapies (13,14). Therefore, a large number of DWI studies have focused on estimating compartment sizes in biological tissues.

One approach to measure compartment size involves measurement of the diffusion-diffraction pattern resulting from restricted water molecules in the long-diffusion time limit and short-gradient pulse approximation (15). The diffraction pattern has been reported to successfully characterize the cell sizes of mono-dispersed erythrocytes (16), but fails in most real biological tissues due to the heterogeneous distribution of cell sizes. A related approach, Q-space imaging, generates a displacement probability distribution function that can provide apparent compartment sizes in biological tissues, but tends to overestimate cell size due to the inability to separate the signal contributions from intra- and extra-cellular spaces (17,18) and violation of the short-gradient pulse approximation (19).

An alternative approach is to develop a geometric model of tissue microstructure which allows more accurate estimates of cell size and several other morphological properties. Models that include more than one compartment with or without the effects of membrane permeability have been used to assess axon sizes in bovine optic nerve (20), to characterize axon size distributions in vitro (21) and in vivo (22), to quantify mean axon size in the corpus callosum of human (23) and monkey brain (24), and to measure cell size in a solid tumor (25). These studies used conventional pulsed gradient spin echo (PGSE) pulse sequences, whereas double diffusion encoding (DDE) and oscillating gradient spin echo (OGSE) sequences have also been used to measure cell sizes in fixed yeast cells in vitro (26) and fixed tissues ex vivo (27). Most of these techniques have been applied to measure axon sizes smaller than 10 μm, with less emphasis on assessing cells in solid tumors, which typically range from 10 to 20 μm.

Recently, we reported a temporal diffusion spectroscopy (TDS) based approach (28) that combines PGSE (long diffusion times) and OGSE (short diffusion times) acquisitions to cover a specific range of effective diffusion times that allows reliable quantification of microstructure at length scales of 10 to 20 μm, i.e., typical cancer cell size. We term this new approach Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion (IMPULSED) and have demonstrated that it can accurately quantify cell sizes in cell cultures in vitro (28). Here, IMPULSED is applied in vivo to estimate microstructural features, including cell size and cellularity, in three different colorectal cancer xenograft tumor models (DiFi, HCT116, and SW620) with different cell sizes and cellularities (29,30). Moreover, imaging measurements are validated by histologic analyses based on Na/K-ATPase immunostaining of the cell membrane, which overcomes major drawbacks of conventional staining such as H&amp;E in estimating cell size of densely-packed cancerous tissues.

Methods

Diffusion signal model

We assume that the diffusion weighted signals of cell samples can be expressed as the sum of signals arising from intra- and extracellular spaces, namely,

S = vin × Sin + (1 − vin) × Sex,
(1)

where vin is the water volume fraction of intracellular space, and Sin and Sex are the signal magnitudes per volume from the intra- and extracellular spaces, respectively. The water exchange between intra- and extracellular spaces is omitted, as suggested in numerous diffusion MRI biophysical models of tumors (25,28).

Following previous approaches (25,28), tumors are modeled as densely-packed spherical cells. Note that the significant variations of cell shapes in realistic tissues may not affect our fitting results if an effective mean cell size is defined (28). The analytical expressions of OGSE signals in some typical geometrical structures, e.g. cylinders and spheres, have been derived previously using a Gaussian approximation for the phase distribution (31,32). For OGSE measurements of diffusion within impermeable spheres using cosine-modulated gradient waveforms, the intracellular diffusion signal can be expressed as

Sin(OGSE)=exp(2(γg)2nBnλn2Din2(λn2Din2+4π2f2)2{(λn2Din2+4π2f2)λnDin[δ2+sin(4πfδ)8πf]1+exp(λnDinδ)+exp(λnDinΔ)(1cosh(λnDinδ))})
(2)

where Din is the intracellular diffusion coefficient, f is the oscillation frequency, δ is the gradient duration, Δ is the separation of two diffusion gradients, g is the gradient amplitude, and λn and Bn are structure dependent parameters related to the the spherical cell diameter d. The expressions of λn and Bn have been reported previously (31,33). The accuracy of Eq.(2) has been validated by computer simulations (31,32) and phantom experiments (34).

For PGSE measurements of diffusion within impermeable spheres, the intracellular diffusion signal can be expressed as a specific case (f➔0) of Eq.(2)

Sin(PGSE)=exp(2(γgDin)2nBnλn2{λnDinδ1+exp(λnDinδ)+exp(λnDinΔ)(1cosh(λnDinδ))})
(3)

which has been reported previously (33).

Eqs.(2) and (3) describe intracellular diffusion signals obtained using OGSE and PGSE methods, respectively, and the spherical cell diameter d can be fit using these equations.

Because only a narrow range of frequencies are achievable in practice, the ADC values of the extracellular space show a linear dependence on the oscillating-gradient frequency (35,36). As a result, the extracellular diffusion signal can be modeled as shown in Equation 4, namely,

Sex(OGSE) = exp[−b(Dex0 + βexf)],
(4)

where Dex0 is the extracellular diffusion rate at frequencies close to 0, and βex is the slope of extracellular diffusion coefficient with respect to frequency f, which contains information on structural dimensions. The extracellular diffusion signal measured by PGSE sequence can be obtained as f approaches zero in Eq.(4):

Sex(PGSE) = exp[−bDex0]
(5)

In vivo tumor models

All animal procedures were approved by the Institutional Animal Care and Usage Committee at Vanderbilt University. Female athymic nude mice (Harlan Laboratories, Inc., Indianapolis, IN) were used for the study and observed daily and weighed weekly to ensure that interventions were well tolerated. A total of ten mice were inoculated with either DiFi (n=3), HCT116 (n=4), or SW620 (n=3) cells into the right hind limb. When each tumor reached a size of 200–300 mm, the MR imaging was performed as described below, and the mouse was euthanized for histology immediately afterwards.

In Vivo MR Imaging

Mice were anesthetized with a 2%/98% isoflurane/oxygen mixture before and during scanning using a Varian DirectDrive™ horizontal 4.7 T magnet (Varian Inc., Palo Alto, CA). The magnet bore temperature was kept at 32°C using a warm-air feedback system. Stretchable medical tape was used to ensure the proper positioning of hind limbs and tumors and to restrain movement caused by respiration, as well as to reduce motion-induced artifacts in the image data. Respiratory signals were monitored using a small pneumatic pillow placed under the mouse abdomen and respiration gating (SA Instruments, Stony Brook, NY) was applied to further reduce motion artifacts. A doped water solution (5 mM CuSO4) was placed beneath the animal at thermal equilibrium with the magnet bore temperature, and its ADC value was measured to monitor the consistency of ADC measurements.

Both OGSE and PGSE sequences were implemented using a 2-shot echo planar imaging (EPI) acquisition. The imaging parameters for PGSE acquisitions were diffusion gradient durations δ = 4 ms, and separation Δ = 48 ms. The OGSE sequence used gradient frequencies from 50–150 Hz with δ/Δ = 20/25 ms, corresponding to effective diffusion times (1/4f, where f is the frequency (37)) approximately from 5 to 1.7 ms. As shown in Table 1, five b values at equal logarithmic spacing from 0 to either 2000 sec/mm or the allowed maximum b value, limited by our maximum gradient strength of 360 mT/m in a single direction, were used for both PGSE and OGSE acquisitions. Multiple axial slices covering the entire tumor of each animal were acquired with a slice thickness of 2 mm. The matrix size was 128×64 with FOV= 40×20 mm, yielding an isotropic in-plane resolution of 312.5 um. Note that the echo times (echo time = 67 ms) for all diffusion measurements were the same to minimize differential relaxation effects.

Table 1

b-values used in PGSE and OGSE acquisitions.

Acquisitionb-values (ms/μm)
PGSE0, 0.5, 1, 1.5, 2
50 Hz OGSE0, 0.5, 1, 1.5, 2
100 Hz OGSE0, 0.33, 0.66, 1, 1.32
150 Hz OGSE0, 0.15, 0.3, 0.45, 0.6

Histology

The animals were sacrificed immediately after each MRI session. The tumors were then dissected, cut into small pieces of approximately 2 mm in thickness, fixed in 10% formalin for 24 hours and transferred to 70% ethanol prior to paraffin embedding. Tissues were then sectioned (8 μm thickness) and stained with hematoxylin and eosin (H&amp;E) or Na/K-ATPase (ab76020, Abcam).

Na/K-ATPase is a plasma membrane pump responsible for the extracellular transport of sodium ions and the intracellular transport of potassium ions. It is one of the most widely expressed plasma membrane markers (38) which provides opportunities to better visualize cell boundaries (membranes) under the circumstances that cancer cells are densely packed in solid tumors. Briefly, tissue samples were de-paraffinized, rehydrated, and antigen retrieval was performed using 6.1 pH citrate buffer (S169984-2, Dako) for 20 minutes at 105°C in a pressure cooker followed by a 10 minute bench cool down. Samples were treated with 3% hydrogen peroxide, and blocked for 30 minutes in PBS/3% bovine serum albumin/10% donkey serum. Primary antibody was incubated overnight at 4°C followed by secondary antibody detection with Cy7-anti-rabbit (Na/K-ATPase) labelled antibodies and DAPI.

The capability of conventional microscopy of glass slides to estimate the structural features of whole tumor tissues is limited by the insufficient sampling of microscopy sections (39). In the current study, the whole stained slides were scanned by a Leica SCN400 Slide Scanner with a magnification of 20 to generate high-resolution digital images covering the whole tumor. A purpose-written segmentation algorithm was implemented to calculate the cell size and total number of cells for the entire slides. In this way, a more accurate histological characterization of tumor tissues were obtained with minimized influences of choices of regions of interest due to tumor heterogeneity.

Data analysis

Eq. (1)(4) with five unknown variables: cell size d, intracellular diffusion coefficient Din, intracellular volume fraction vin, and extracellular parameters Dex0 and βex (see Eq.(4)) were fit to the PGSE and OGSE diffusion signals for each voxel in tumors, using the lsqcurvefit function in Matlab (Mathworks, Natick, MA). The constraints for fitting parameters were based on physiologically relevant values : 0 ≤ d ≤ 40 μm, 0≤ vin ≤ 1, 0 ≤ Din ≤3.0 μm/ms, 0 ≤ Dex0 ≤ 3.0 μm/ms, and 0 ≤ βex ≤ 10 μm. Randomly-generated initial parameter values were used. To ensure the global minimum was reached, the fitting was repeated 100 times for each sample, and the analyses corresponding to the smallest fitting residual were chosen as the final results.

The three dimensional tumor cell density ρ was estimated as

ρ=6vinπd3
(2)

However, tumor cellularity (the total number of cells in a unit area of 2D tissue section) is typically used in pathological analysis in clinics. In order to compare IMPULSED-derived parameters with histology, we converted the tumor cell density to the tumor cellularity by assuming that solid tumors consist of spherical cancer cells densely-packed on a face-center-cube grid (5,40), and hence

cellularity=2×(3vin2π)23/d2
(3)

Statistical Analysis

The differences in histology-derived cell size and cellularity, IMPULSED-derived parameters, and ADC values among three different types of tumor cell lines were summarized using means and standard deviations, and compared by one-way ANOVA. All the tests were two-sided and a FDR (False Discovery Rate) adjusted p-value of 0.05 or less was taken to indicate statistical significance with consideration of multiple comparisons. The correlations between i) histology and IMPULSED-derived cellularities; ii) histology-derived cellularities and PGSE-derived ADC values were assessed using Spearman’s tau correlation coefficient (41). Statistical analyses were performed using OriginPro 9.0 (OriginLab. Northampton, MA).

Diffusion signal model

We assume that the diffusion weighted signals of cell samples can be expressed as the sum of signals arising from intra- and extracellular spaces, namely,

S = vin × Sin + (1 − vin) × Sex,
(1)

where vin is the water volume fraction of intracellular space, and Sin and Sex are the signal magnitudes per volume from the intra- and extracellular spaces, respectively. The water exchange between intra- and extracellular spaces is omitted, as suggested in numerous diffusion MRI biophysical models of tumors (25,28).

Following previous approaches (25,28), tumors are modeled as densely-packed spherical cells. Note that the significant variations of cell shapes in realistic tissues may not affect our fitting results if an effective mean cell size is defined (28). The analytical expressions of OGSE signals in some typical geometrical structures, e.g. cylinders and spheres, have been derived previously using a Gaussian approximation for the phase distribution (31,32). For OGSE measurements of diffusion within impermeable spheres using cosine-modulated gradient waveforms, the intracellular diffusion signal can be expressed as

Sin(OGSE)=exp(2(γg)2nBnλn2Din2(λn2Din2+4π2f2)2{(λn2Din2+4π2f2)λnDin[δ2+sin(4πfδ)8πf]1+exp(λnDinδ)+exp(λnDinΔ)(1cosh(λnDinδ))})
(2)

where Din is the intracellular diffusion coefficient, f is the oscillation frequency, δ is the gradient duration, Δ is the separation of two diffusion gradients, g is the gradient amplitude, and λn and Bn are structure dependent parameters related to the the spherical cell diameter d. The expressions of λn and Bn have been reported previously (31,33). The accuracy of Eq.(2) has been validated by computer simulations (31,32) and phantom experiments (34).

For PGSE measurements of diffusion within impermeable spheres, the intracellular diffusion signal can be expressed as a specific case (f➔0) of Eq.(2)

Sin(PGSE)=exp(2(γgDin)2nBnλn2{λnDinδ1+exp(λnDinδ)+exp(λnDinΔ)(1cosh(λnDinδ))})
(3)

which has been reported previously (33).

Eqs.(2) and (3) describe intracellular diffusion signals obtained using OGSE and PGSE methods, respectively, and the spherical cell diameter d can be fit using these equations.

Because only a narrow range of frequencies are achievable in practice, the ADC values of the extracellular space show a linear dependence on the oscillating-gradient frequency (35,36). As a result, the extracellular diffusion signal can be modeled as shown in Equation 4, namely,

Sex(OGSE) = exp[−b(Dex0 + βexf)],
(4)

where Dex0 is the extracellular diffusion rate at frequencies close to 0, and βex is the slope of extracellular diffusion coefficient with respect to frequency f, which contains information on structural dimensions. The extracellular diffusion signal measured by PGSE sequence can be obtained as f approaches zero in Eq.(4):

Sex(PGSE) = exp[−bDex0]
(5)

In vivo tumor models

All animal procedures were approved by the Institutional Animal Care and Usage Committee at Vanderbilt University. Female athymic nude mice (Harlan Laboratories, Inc., Indianapolis, IN) were used for the study and observed daily and weighed weekly to ensure that interventions were well tolerated. A total of ten mice were inoculated with either DiFi (n=3), HCT116 (n=4), or SW620 (n=3) cells into the right hind limb. When each tumor reached a size of 200–300 mm, the MR imaging was performed as described below, and the mouse was euthanized for histology immediately afterwards.

In Vivo MR Imaging

Mice were anesthetized with a 2%/98% isoflurane/oxygen mixture before and during scanning using a Varian DirectDrive™ horizontal 4.7 T magnet (Varian Inc., Palo Alto, CA). The magnet bore temperature was kept at 32°C using a warm-air feedback system. Stretchable medical tape was used to ensure the proper positioning of hind limbs and tumors and to restrain movement caused by respiration, as well as to reduce motion-induced artifacts in the image data. Respiratory signals were monitored using a small pneumatic pillow placed under the mouse abdomen and respiration gating (SA Instruments, Stony Brook, NY) was applied to further reduce motion artifacts. A doped water solution (5 mM CuSO4) was placed beneath the animal at thermal equilibrium with the magnet bore temperature, and its ADC value was measured to monitor the consistency of ADC measurements.

Both OGSE and PGSE sequences were implemented using a 2-shot echo planar imaging (EPI) acquisition. The imaging parameters for PGSE acquisitions were diffusion gradient durations δ = 4 ms, and separation Δ = 48 ms. The OGSE sequence used gradient frequencies from 50–150 Hz with δ/Δ = 20/25 ms, corresponding to effective diffusion times (1/4f, where f is the frequency (37)) approximately from 5 to 1.7 ms. As shown in Table 1, five b values at equal logarithmic spacing from 0 to either 2000 sec/mm or the allowed maximum b value, limited by our maximum gradient strength of 360 mT/m in a single direction, were used for both PGSE and OGSE acquisitions. Multiple axial slices covering the entire tumor of each animal were acquired with a slice thickness of 2 mm. The matrix size was 128×64 with FOV= 40×20 mm, yielding an isotropic in-plane resolution of 312.5 um. Note that the echo times (echo time = 67 ms) for all diffusion measurements were the same to minimize differential relaxation effects.

Table 1

b-values used in PGSE and OGSE acquisitions.

Acquisitionb-values (ms/μm)
PGSE0, 0.5, 1, 1.5, 2
50 Hz OGSE0, 0.5, 1, 1.5, 2
100 Hz OGSE0, 0.33, 0.66, 1, 1.32
150 Hz OGSE0, 0.15, 0.3, 0.45, 0.6

Histology

The animals were sacrificed immediately after each MRI session. The tumors were then dissected, cut into small pieces of approximately 2 mm in thickness, fixed in 10% formalin for 24 hours and transferred to 70% ethanol prior to paraffin embedding. Tissues were then sectioned (8 μm thickness) and stained with hematoxylin and eosin (H&amp;E) or Na/K-ATPase (ab76020, Abcam).

Na/K-ATPase is a plasma membrane pump responsible for the extracellular transport of sodium ions and the intracellular transport of potassium ions. It is one of the most widely expressed plasma membrane markers (38) which provides opportunities to better visualize cell boundaries (membranes) under the circumstances that cancer cells are densely packed in solid tumors. Briefly, tissue samples were de-paraffinized, rehydrated, and antigen retrieval was performed using 6.1 pH citrate buffer (S169984-2, Dako) for 20 minutes at 105°C in a pressure cooker followed by a 10 minute bench cool down. Samples were treated with 3% hydrogen peroxide, and blocked for 30 minutes in PBS/3% bovine serum albumin/10% donkey serum. Primary antibody was incubated overnight at 4°C followed by secondary antibody detection with Cy7-anti-rabbit (Na/K-ATPase) labelled antibodies and DAPI.

The capability of conventional microscopy of glass slides to estimate the structural features of whole tumor tissues is limited by the insufficient sampling of microscopy sections (39). In the current study, the whole stained slides were scanned by a Leica SCN400 Slide Scanner with a magnification of 20 to generate high-resolution digital images covering the whole tumor. A purpose-written segmentation algorithm was implemented to calculate the cell size and total number of cells for the entire slides. In this way, a more accurate histological characterization of tumor tissues were obtained with minimized influences of choices of regions of interest due to tumor heterogeneity.

Data analysis

Eq. (1)(4) with five unknown variables: cell size d, intracellular diffusion coefficient Din, intracellular volume fraction vin, and extracellular parameters Dex0 and βex (see Eq.(4)) were fit to the PGSE and OGSE diffusion signals for each voxel in tumors, using the lsqcurvefit function in Matlab (Mathworks, Natick, MA). The constraints for fitting parameters were based on physiologically relevant values : 0 ≤ d ≤ 40 μm, 0≤ vin ≤ 1, 0 ≤ Din ≤3.0 μm/ms, 0 ≤ Dex0 ≤ 3.0 μm/ms, and 0 ≤ βex ≤ 10 μm. Randomly-generated initial parameter values were used. To ensure the global minimum was reached, the fitting was repeated 100 times for each sample, and the analyses corresponding to the smallest fitting residual were chosen as the final results.

The three dimensional tumor cell density ρ was estimated as

ρ=6vinπd3
(2)

However, tumor cellularity (the total number of cells in a unit area of 2D tissue section) is typically used in pathological analysis in clinics. In order to compare IMPULSED-derived parameters with histology, we converted the tumor cell density to the tumor cellularity by assuming that solid tumors consist of spherical cancer cells densely-packed on a face-center-cube grid (5,40), and hence

cellularity=2×(3vin2π)23/d2
(3)

Statistical Analysis

The differences in histology-derived cell size and cellularity, IMPULSED-derived parameters, and ADC values among three different types of tumor cell lines were summarized using means and standard deviations, and compared by one-way ANOVA. All the tests were two-sided and a FDR (False Discovery Rate) adjusted p-value of 0.05 or less was taken to indicate statistical significance with consideration of multiple comparisons. The correlations between i) histology and IMPULSED-derived cellularities; ii) histology-derived cellularities and PGSE-derived ADC values were assessed using Spearman’s tau correlation coefficient (41). Statistical analyses were performed using OriginPro 9.0 (OriginLab. Northampton, MA).

Results

Histological characterization of cell sizes and cellularities of DiFi, HCT116, and SW620 tumors

Representative raw (top) and segmented (bottom) H&amp;E stained slides for a DiFi tumor are shown in Figure1A. The mean cellularity of each tumor was calculated from the high-resolution digital images of H&amp;E-stained slides by counting the segmented nuclei. Figure 2A shows that SW620 tumors have a higher average cellularity than DiFi and HCT116 tumors (p < 0.05).

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(A) Typical raw (left) and segmented (right) H&amp;E stained histological images for a DiFi tumor. Nuclei were labelled in brown; (B) Typical raw (left) and segmented (right) Na/K-ATPase stained histological images for DiFi, HCT116, and SW620 tumors. Nuclei were visualized with DAPI (blue). Note that all the cells express high level, relative evenly distributed Na/K-ATPase (green) on their plasma membranes. Staining on this target enables a clear delineation (white contours) of cell boundaries.

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Histology-derived tumor cellularity (A) and area weighted cell size (B) for DiFi, HCT116, and SW620 tumors, mean ± sd. *P<0.05 as measured by one-way ANOVA with a FDR (False Discovery Rate) posttest.

Although the cytoplasm is colored in red on H&amp;E stained images, the cell boundaries are difficult to identify due to very narrow extracellular spaces in solid tumors. To overcome this practical problem, the cell membranes were visualized in green with immunofluorescence staining for Na/K-ATPase as shown in the left panel of Figure 1B. The cell size can be obtained from each segmented cell (right panel of Figure 1B) and the area weighted cell sizes (= n=1Ndn3n=1Ndn2, where N is the total number of cells and dn is the cell size of the n cell (23)) for DiFi, HCT116, and SW620 tumors are summarized in Figure 2B. The mean cancer cell size of SW620 tumors (11.07 ± 0.42 μm) is significantly (p < 0.05) smaller than that of DiFi tumors (13.72 ± 0.76 μm).

Microstructural characterization of tumors using IMPULSED method

Representative OGSE and PGSE single-voxel signals from DiFi, HCT116, and SW620 tumors are shown in Figure 3. As expected, the diffusion-weighted signals decay faster as the effective diffusion time decreases. The PGSE signals were significantly higher than OGSE signals, indicating that lower effective diffusion rates were obtained at longer diffusion times. The solid lines represent the fits from Eq (1). The fitted IMPULSED parameters and PGSE-derived ADC for the signals shown in Figure 3 are listed in Table 2.

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Typical OGSE (50, 100, and 150 Hz) and PGSE signals for voxels from DiFi, HCT116, and SW620 tumors (from left to right). The solid line represents the fit using Eq(1)(4).

Table 2

IMPULSED-derived parameters (d, vin, Din, Dex0, βex) and PGSE-derived ADC with 95% confidence intervals for typical single-voxel signals from DiFi, HCT116, and SW620 tumors.

d
(μm)
vinDin
(μm/ms)
Dex0
(μm/ms)
βex
(μm)
PGSE-derived ADC
(μm/ms)
DiFi18.95±1.610.86±0.131.15±0.340.44±0.122.13±1.340.40±0.02
HCT11613.51±1.180.46±0.111.53±0.450.75±0.182.36±1.760.44±0.03
SW62011.52±1.420.49±0.110.87±0.240.80±0.215.67±2.760.33±0.02

An H&amp;E stained histological image, PGSE-derived ADC map, and IMPULSED-derived parametric maps (apparent cellularity, d, vin, Din, Dex0, and βex) of a representative slice through a tumor are shown in Figure 4. It is evident that the H&amp;E stained tumor image shows cell density heterogeneity. The PGSE-derived ADC and IMPULSED-derived parametric maps show similar patterns to the histological image, consistent with the biological interpretations of these parameters. For a quantitative comparison, the detailed statistics of five fitted parameters, PGSE-derived ADC and IMPULSED-derived cellularities for three types of tumors are summarized in a set of box plots (Figure 5). The cell sizes for DiFi, HCT116, and SW620, are 16.1±3.31, 14.21±4.46, and 11.69±2.42 μm, respectively (Figure 5A), close to our histological results. The intracellular volume fractions of DiFi tumors are significantly higher than HCT116 tumors (P<0.01, Figure 5C). The Dex0 of DiFi tumors are significantly higher than SW620 (P<0.05, Figure 5D). There are no significant differences in Din and βex among the three types of tumors (P>0.05, Figure 5B&amp;E). SW620 tumors have the lowest PGSE-derived ADC values, indicating the highest cell density among these three types of tumors (P<0.05, Figure 5F). The IMPULSED-derived cellularity of SW620 tumors are significantly higher than HCT116 and DiFi tumors (P<0.05, Figure 5G).

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H&amp;E stained histological image, PGSE-derived ADC map, and IMPULSED-derived parametric maps (apparent cellularity, d, vin, Din, Dex0, and βex) of a representative slice through tumor, overlaid on T2-weighted MR images.

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Box-and-whisker plots of the fitted d, vin, Din, Dex0, and βex, PGSE-derived ADC values, and IMPULSED-derived cellularites for DiFi, HCT116, and SW620 tumors. For all the Box-and-whisker plots, the 25–75 percentiles are blocked by the box, the black and red bands inside the box are the median and mean, respectively, and the whiskers mark the SD. *P<0.05 and **P<0.01 as measured by one-way ANOVA with a FDR (False Discovery Rate) posttest.

IMPULSED-derived apparent cellularity correlates well with histological results

A single ADC value obtained with a PGSE acquisition at a relatively long diffusion time (e.g., 48 ms in the current study) has long been considered to negatively correlate with cellularity. On the other hand, an apparent cellularity can be specifically estimated using Eq.[3]. Figure 6A&amp;B displays the correlations between histology and IMPULSED-derived cellularity, and histology and PGSE-derived ADC for each animal. The positive correlation (Spearman’s correlation coefficient = 0.81, P < 0.0001) between histology and IMPULSED-derived cellularity is much stronger than the negative correlation (Spearman’s correlation coefficient = −0.69, P = 0.03) between histology and PGSE-derived ADC, suggesting IMPULSED-derived cellularity is a more specific indicator of tumor cellularity compared with ADC, while the latter is influenced by multiple microstructural parameters simultaneously.

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(A) Correlation between histological-derived cellularities and PGSE-derived ADC values for all the tumors. (B) Correlation between histological-derived cellularities and IMPULSED-derived apparent cellularities for all the tumors. The dot line represents the linear fit.

Histological characterization of cell sizes and cellularities of DiFi, HCT116, and SW620 tumors

Representative raw (top) and segmented (bottom) H&amp;E stained slides for a DiFi tumor are shown in Figure1A. The mean cellularity of each tumor was calculated from the high-resolution digital images of H&amp;E-stained slides by counting the segmented nuclei. Figure 2A shows that SW620 tumors have a higher average cellularity than DiFi and HCT116 tumors (p < 0.05).

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(A) Typical raw (left) and segmented (right) H&amp;E stained histological images for a DiFi tumor. Nuclei were labelled in brown; (B) Typical raw (left) and segmented (right) Na/K-ATPase stained histological images for DiFi, HCT116, and SW620 tumors. Nuclei were visualized with DAPI (blue). Note that all the cells express high level, relative evenly distributed Na/K-ATPase (green) on their plasma membranes. Staining on this target enables a clear delineation (white contours) of cell boundaries.

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Histology-derived tumor cellularity (A) and area weighted cell size (B) for DiFi, HCT116, and SW620 tumors, mean ± sd. *P<0.05 as measured by one-way ANOVA with a FDR (False Discovery Rate) posttest.

Although the cytoplasm is colored in red on H&amp;E stained images, the cell boundaries are difficult to identify due to very narrow extracellular spaces in solid tumors. To overcome this practical problem, the cell membranes were visualized in green with immunofluorescence staining for Na/K-ATPase as shown in the left panel of Figure 1B. The cell size can be obtained from each segmented cell (right panel of Figure 1B) and the area weighted cell sizes (= n=1Ndn3n=1Ndn2, where N is the total number of cells and dn is the cell size of the n cell (23)) for DiFi, HCT116, and SW620 tumors are summarized in Figure 2B. The mean cancer cell size of SW620 tumors (11.07 ± 0.42 μm) is significantly (p < 0.05) smaller than that of DiFi tumors (13.72 ± 0.76 μm).

Microstructural characterization of tumors using IMPULSED method

Representative OGSE and PGSE single-voxel signals from DiFi, HCT116, and SW620 tumors are shown in Figure 3. As expected, the diffusion-weighted signals decay faster as the effective diffusion time decreases. The PGSE signals were significantly higher than OGSE signals, indicating that lower effective diffusion rates were obtained at longer diffusion times. The solid lines represent the fits from Eq (1). The fitted IMPULSED parameters and PGSE-derived ADC for the signals shown in Figure 3 are listed in Table 2.

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Typical OGSE (50, 100, and 150 Hz) and PGSE signals for voxels from DiFi, HCT116, and SW620 tumors (from left to right). The solid line represents the fit using Eq(1)(4).

Table 2

IMPULSED-derived parameters (d, vin, Din, Dex0, βex) and PGSE-derived ADC with 95% confidence intervals for typical single-voxel signals from DiFi, HCT116, and SW620 tumors.

d
(μm)
vinDin
(μm/ms)
Dex0
(μm/ms)
βex
(μm)
PGSE-derived ADC
(μm/ms)
DiFi18.95±1.610.86±0.131.15±0.340.44±0.122.13±1.340.40±0.02
HCT11613.51±1.180.46±0.111.53±0.450.75±0.182.36±1.760.44±0.03
SW62011.52±1.420.49±0.110.87±0.240.80±0.215.67±2.760.33±0.02

An H&amp;E stained histological image, PGSE-derived ADC map, and IMPULSED-derived parametric maps (apparent cellularity, d, vin, Din, Dex0, and βex) of a representative slice through a tumor are shown in Figure 4. It is evident that the H&amp;E stained tumor image shows cell density heterogeneity. The PGSE-derived ADC and IMPULSED-derived parametric maps show similar patterns to the histological image, consistent with the biological interpretations of these parameters. For a quantitative comparison, the detailed statistics of five fitted parameters, PGSE-derived ADC and IMPULSED-derived cellularities for three types of tumors are summarized in a set of box plots (Figure 5). The cell sizes for DiFi, HCT116, and SW620, are 16.1±3.31, 14.21±4.46, and 11.69±2.42 μm, respectively (Figure 5A), close to our histological results. The intracellular volume fractions of DiFi tumors are significantly higher than HCT116 tumors (P<0.01, Figure 5C). The Dex0 of DiFi tumors are significantly higher than SW620 (P<0.05, Figure 5D). There are no significant differences in Din and βex among the three types of tumors (P>0.05, Figure 5B&amp;E). SW620 tumors have the lowest PGSE-derived ADC values, indicating the highest cell density among these three types of tumors (P<0.05, Figure 5F). The IMPULSED-derived cellularity of SW620 tumors are significantly higher than HCT116 and DiFi tumors (P<0.05, Figure 5G).

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H&amp;E stained histological image, PGSE-derived ADC map, and IMPULSED-derived parametric maps (apparent cellularity, d, vin, Din, Dex0, and βex) of a representative slice through tumor, overlaid on T2-weighted MR images.

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Box-and-whisker plots of the fitted d, vin, Din, Dex0, and βex, PGSE-derived ADC values, and IMPULSED-derived cellularites for DiFi, HCT116, and SW620 tumors. For all the Box-and-whisker plots, the 25–75 percentiles are blocked by the box, the black and red bands inside the box are the median and mean, respectively, and the whiskers mark the SD. *P<0.05 and **P<0.01 as measured by one-way ANOVA with a FDR (False Discovery Rate) posttest.

IMPULSED-derived apparent cellularity correlates well with histological results

A single ADC value obtained with a PGSE acquisition at a relatively long diffusion time (e.g., 48 ms in the current study) has long been considered to negatively correlate with cellularity. On the other hand, an apparent cellularity can be specifically estimated using Eq.[3]. Figure 6A&amp;B displays the correlations between histology and IMPULSED-derived cellularity, and histology and PGSE-derived ADC for each animal. The positive correlation (Spearman’s correlation coefficient = 0.81, P < 0.0001) between histology and IMPULSED-derived cellularity is much stronger than the negative correlation (Spearman’s correlation coefficient = −0.69, P = 0.03) between histology and PGSE-derived ADC, suggesting IMPULSED-derived cellularity is a more specific indicator of tumor cellularity compared with ADC, while the latter is influenced by multiple microstructural parameters simultaneously.

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(A) Correlation between histological-derived cellularities and PGSE-derived ADC values for all the tumors. (B) Correlation between histological-derived cellularities and IMPULSED-derived apparent cellularities for all the tumors. The dot line represents the linear fit.

Discussion

Cellularity and cell size in biological tissues play important roles in the diagnosis and prognosis of cancer. Conventionally, these parameters are measured from invasive biopsies, which suffer from major limitations. In this paper, it is demonstrated that the IMPULSED method allows an accurate in vivo quantification of cell size. The IMPULSED-derived cell sizes are slightly larger than the histology-derived area weighted cell sizes. This discrepancy can be explained by a combination of tissue shrinkage during histology preparation and the fact that the tissue section rarely passes through the center of the cell, leading to an underestimation of cell size. The degree of the underestimation increases as the cell size increases, and as a result, DiFi tumors have the largest difference between histology and IMPULSED-derived cell sizes. The cell sizes of HCT116 and SW620 have also been measured in vitro by light microscopy and reported to be 14.40±3.88 and 11.09±1.58 μm (29,30), consistent with our MR results.

ADC values obtained with a PGSE sequence at a relatively long diffusion time (20–80 ms) have previously been negatively correlated with cellularity. However, they are not always correlated with cellularity (42,43). For example, increased/decreased ADCs in tumor tissues due to treatment-induced cell shrinkage/swelling have been reported previously. IMPULSED method extracts the cell size and intracellular volume fraction from multiple ADC values and provides a more direct measurement of the tumor cellularity, independent of cancer cell size. The IMPULSED-derived apparent cellularity is demonstrated (Figure 6) to be a more specific indicator of cellularity in tumor tissues than conventional ADC values.

Recently, VERDICT, a PGSE based method, has been used to quantify microstructural properties (e.g., cell size and intracellular volume fraction) in tumors (25,44). However, this method requires prior knowledge of intra/extra-cellular diffusivities in order to minimize fitting errors (44). As demonstrated recently (45), it is challenging for these PGSE based methods to measure cell size and intracellular diffusivity simultaneously, presumably due the relatively long diffusion times used in PGSE measurements. The incorporation of OGSE acquisitions increases the sensitivity to intracellular diffusion, which in turn provides extra microstructural information compared with methods with PGSE measurements only. In addition, it has been reported (46) that low-frequency OGSE sequences provide more sensitivity to the axon diameter than PGSE sequences when axons have unknown and dispersed orientations. This conclusion may also be true when measuring the tumor cell size if the cells are modeled as ellipsoids. Therefore, the IMPULSED method provides more comprehensive microstructural information about tumors at broader length scales, and thus may be a plausible way to characterize tumor status.

The water exchange between intra and extracellular spaces was assumed negligible in the current study. This assumption has been shown to be reasonable in previous OGSE studies (4749), because the effective diffusion time of the OGSE measurement is usually much shorter (< 5 ms) compared with the intracellular lifetime of water molecules (50,51). However, the precise effect of water exchange on diffusion measurements in vivo remains unclear. The incorporation of PGSE measurements with a long diffusion time makes this method more likely to be affected by water exchange than typical OGSE methods. As reported in our previous in vitro study, the ignorance of membrane permeability is likely to underestimate the fitted intracellular volume fraction without affecting the accuracy of cell size measurement (28). In the current study, the fitted intracellular volume fractions are about 65%, 45%, and 55% for DiFi, HCT116, and SW620 tumors, respectively, which are lower than typical intracellular volume fractions in tumor tissues reported previously. Such an underestimation of intracellular volume leads to an underestimation of cellularities, as shown in Figure 6B. In addition, transcytolemmal water exchange increases significantly in developing/treated tumors, especially apoptotic regions (52). Therefore, the influence of transcytolemmal water exchange on quantification of microstructural parameters in tumor tissues using the IMPULSED method needs to be further investigated. Either a more complex model which accounts for water exchange between intra and extracellular spaces, such as the Karger model (53), or another independent measurement of water exchange effects, such as filter exchange imaging (FEXI), may be included in future in vivo studies.

Capillary perfusion was assumed negligible in the current study. This assumption has been used in many cancer studies using DW-MRI (5,6), because the perfusion fraction of tissues is usually much smaller than the diffusion fraction of tissues. In cases where effects resulted from tumor angiogenesis on ADC measurements cannot be assumed negligible, the current PGSE/OGSE sequences can be modified to acquire perfusion-free MR signals by inserting a PGSE filter with a small b value at the beginning of the sequence (7).

High resolution histology images typically require high magnifications such as 20X or 40X, which in turn significantly limits the histology analyses based on small regions-of-interest (ROIs). However, most tumors are very heterogeneous, and hence the choices of ROIs in histological analyses remarkably affect the results. To reduce the influences of this error source, whole slide imaging was used in the current work to acquire high magnification (20X) digital images of whole histological slides of tumor tissues. Note that due to the challenges in the co-registration between histology and MRI of deformable xenografts in mouse hind limbs, all histology- and MRI-derived parameters were averaged for each tumor for comparison and correlation in the current work. For even better accuracy, it is plausible to perform a voxel-wise correlation between histology and MRI in future studies.

Conclusion

A temporal diffusion spectroscopy based approach (IMPULSED method), combining a single long diffusion time PGSE and low-frequency OGSE measurements, was developed for accurately measuring relatively large cell sizes (10–20 μm) in vivo. Using this method, accurate cell sizes in three types of human colon cancer tumors (DiFi, HCT116, and SW620) were obtained and confirmed by histologic analyses. Apparent cellularities, calculated from the fitted cell sizes and intracellular volume fractions, were shown to have a stronger correlation with histology-derived cellularities than the correlation between conventional PGSE-derived ADC values and histology-derived cellularities. These findings confirm the potential of the IMPULSED method for providing microstructural information non-invasively to assist better characterization and prognosis of cancer.

Acknowledgments

This work was funded by NIH Grants K25CA168936, R01CA109106, R01CA173593, and P50CA128323.

Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA
Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232, USA
Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37232, USA
Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, USA
Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, TN 37232, USA
Department of Medicine, Vanderbilt University Medical Center, Nashville, TN 37232, USA
Corresponding author: Vanderbilt University Institute of Imaging Science, 1161 21st Avenue South, AA 1105 MCN, Nashville, TN 37232-2310, USA. Tel.: +1 615 322 8359; Fax: +1 615 322 0734. ude.tlibrednav@ux.gnohznuj (J. Xu)

Abstract

Purpose

A temporal diffusion MRI spectroscopy based approach has been developed to quantify cancer cell size and density in vivo.

Methods

A novel Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion (IMPULSED) method selects a specific limited diffusion spectral window for an accurate quantification of cell sizes ranging from 10 to 20 μm in common solid tumors. In practice, it is achieved by a combination of a single long diffusion time pulsed gradient spin echo (PGSE) and three low-frequency oscillating gradient spin echo (OGSE) acquisitions. To validate our approach, H&amp;E staining and immunostaining of cell membranes, in concert with whole slide imaging, were used to visualize nuclei and cell boundaries, and hence enabled accurate estimates of cell size and cellularity.

Results

Based on a two compartment model (incorporating intra- and extracellular spaces), accurate estimates of cell sizes were obtained in vivo for three types of human colon cancers. The IMPULSED-derived apparent cellularities showed a stronger correlation (r=−0.81, p<0.0001) with histology-derived cellularities than conventional ADCs (r=−0.69, p<0.03).

Conclusion

The IMPULSED approach samples a specific region of temporal diffusion spectra with enhanced sensitivity to length scales of 10–20 μm, and enables measurements of cell sizes and cellularities in solid tumors in vivo.

Keywords: cell size, density, cellularity, diffusion, MRI, oscillating gradient, diffusion time, IMPULSED, solid tumor
Abstract

References

  • 1. Moffat BA, Chenevert TL, Lawrence TS, Meyer CR, Johnson TD, Dong Q, Tsien C, Mukherji S, Quint DJ, Gebarski SS, Robertson PL, Junck LR, Rehemtulla A, Ross BDFunctional diffusion map: a noninvasive MRI biomarker for early stratification of clinical brain tumor response. Proc Natl Acad Sci U S A. 2005;102(15):5524–5529.[Google Scholar]
  • 2. Gauvain KM, McKinstry RC, Mukherjee P, Perry A, Neil JJ, Kaufman BA, Hayashi RJEvaluating pediatric brain tumor cellularity with diffusion-tensor imaging. Am J Roentgenol. 2001;177(2):449–454.[PubMed][Google Scholar]
  • 3. Sugahara T, Korogi Y, Kochi M, Ikushima I, Shigematu Y, Hirai T, Okuda T, Liang LX, Ge YL, Komohara Y, Ushio Y, Takahashi MUsefulness of diffusion-weighted MRI with echo-planar technique in the evaluation of cellularity in gliomas. Jmri-J Magn Reson Im. 1999;9(1):53–60.[PubMed][Google Scholar]
  • 4. Szafer A, Zhong JH, Gore JCTheoretical-Model for Water Diffusion in Tissues. Magnet Reson Med. 1995;33(5):697–712.[PubMed][Google Scholar]
  • 5. Xu J, Does MD, Gore JCSensitivity of MR diffusion measurements to variations in intracellular structure: effects of nuclear size. Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine/Society of Magnetic Resonance in Medicine. 2009;61(4):828–833.[Google Scholar]
  • 6. Colvin DC, Jourquin J, Xu J, Does MD, Estrada L, Gore JCEffects of intracellular organelles on the apparent diffusion coefficient of water molecules in cultured human embryonic kidney cells. Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine/Society of Magnetic Resonance in Medicine. 2011;65(3):796–801.[Google Scholar]
  • 7. Patterson DM, Padhani AR, Collins DJTechnology insight: water diffusion MRI–a potential new biomarker of response to cancer therapy. Nat Clin Pract Oncol. 2008;5(4):220–233.[PubMed][Google Scholar]
  • 8. Galban CJ, Hoff BA, Chenevert TL, Ross BDDiffusion MRI in early cancer therapeutic response assessment. NMR in biomedicine. 2016[Google Scholar]
  • 9. Alexander DCA general framework for experiment design in diffusion MRI and its application in measuring direct tissue-microstructure features. Magnet Reson Med. 2008;60(2):439–448.[PubMed][Google Scholar]
  • 10. Kozlowski J, Konarzewski M, Gawelczyk ATCell size as a link between noncoding DNA and metabolic rate scaling. P Natl Acad Sci USA. 2003;100(24):14080–14085.[Google Scholar]
  • 11. Baserga RIs cell size important? Cell cycle. 2007;6(7):814–816.[PubMed][Google Scholar]
  • 12. Savage VM, Allen AP, Brown JH, Gillooly JF, Herman AB, Woodruff WH, West GBScaling of number, size, and metabolic rate of cells with body size in mammals. P Natl Acad Sci USA. 2007;104(11):4718–4723.[Google Scholar]
  • 13. Lowe SW, Lin AWApoptosis in cancer. Carcinogenesis. 2000;21(3):485–495.[PubMed][Google Scholar]
  • 14. de Bruin EC, Medema JPApoptosis and non-apoptotic deaths in cancer development and treatment response. Cancer treatment reviews. 2008;34(8):737–749.[PubMed][Google Scholar]
  • 15. Callaghan PT, Coy A, Macgowan D, Packer KJ, Zelaya FODiffraction-Like Effects in Nmr Diffusion Studies of Fluids in Porous Solids. Nature. 1991;351(6326):467–469.[PubMed][Google Scholar]
  • 16. Torres AM, Michniewicz RJ, Chapman BE, Young GA, Kuchel PWCharacterisation of erythrocyte shapes and sizes by NMR diffusion-diffraction of water: correlations with electron micrographs. Magnetic resonance imaging. 1998;16(4):423–434.[PubMed][Google Scholar]
  • 17. Ong HH, Wright AC, Wehrli SL, Souza A, Schwartz ED, Hwang SN, Wehrli FWIndirect measurement of regional axon diameter in excised mouse spinal cord with q-space imaging: Simulation and experimental studies. NeuroImage. 2008;40(4):1619–1632.[Google Scholar]
  • 18. Wang Y, Wang Q, Haldar JP, Yeh FC, Xie MQ, Sun P, Tu TW, Trinkaus K, Klein RS, Cross AH, Song SKQuantification of increased cellularity during inflammatory demyelination. Brain: a journal of neurology. 2011;134:3587–3598.[Google Scholar]
  • 19. Xu JZ, Li H, Harkins KD, Jiang XY, Xie JP, Kang H, Does MD, Gore JCMapping mean axon diameter and axonal volume fraction by MRI using temporal diffusion spectroscopy. NeuroImage. 2014;103:10–19.[Google Scholar]
  • 20. Assaf Y, Cohen YAssignment of the water slow-diffusing component in the central nervous system using q-space diffusion MRS: implications for fiber tract imaging. Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine/Society of Magnetic Resonance in Medicine. 2000;43(2):191–199.[PubMed][Google Scholar]
  • 21. Assaf Y, Blumenfeld-Katzir T, Yovel Y, Basser PJAxCaliber: a method for measuring axon diameter distribution from diffusion MRI. Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine/Society of Magnetic Resonance in Medicine. 2008;59(6):1347–1354.[Google Scholar]
  • 22. Barazany D, Basser PJ, Assaf YIn vivo measurement of axon diameter distribution in the corpus callosum of rat brain. Brain: a journal of neurology. 2009;132(Pt 5):1210–1220.[Google Scholar]
  • 23. Alexander DC, Hubbard PL, Hall MG, Moore EA, Ptito M, Parker GJ, Dyrby TBOrientationally invariant indices of axon diameter and density from diffusion MRI. NeuroImage. 2010;52(4):1374–1389.[PubMed][Google Scholar]
  • 24. Dyrby TB, Sogaard LV, Hall MG, Ptito M, Alexander DCContrast and stability of the axon diameter index from microstructure imaging with diffusion MRI. Magnet Reson Med. 2013;70(3):711–721.[Google Scholar]
  • 25. Panagiotaki E, Walker-Samuel S, Siow B, Johnson SP, Rajkumar V, Pedley RB, Lythgoe MF, Alexander DCNoninvasive Quantification of Solid Tumor Microstructure Using VERDICT MRI. Cancer Res. 2014;74(7):1902–1912.[PubMed][Google Scholar]
  • 26. Shemesh N, Ozarslan E, Basser PJ, Cohen YAccurate noninvasive measurement of cell size and compartment shape anisotropy in yeast cells using double-pulsed field gradient MR. NMR in biomedicine. 2012;25(2):236–246.[Google Scholar]
  • 27. Li H, Jiang X, Wang F, Xu J, Gore JCStructural information revealed by the dispersion of ADC with frequency. Magnetic resonance imaging. 2015;33(9):1083–1090.[Google Scholar]
  • 28. Jiang X, Li H, Xie J, Zhao P, Gore JC, Xu JQuantification of cell size using temporal diffusion spectroscopy. Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine/Society of Magnetic Resonance in Medicine. 2016;75(3):1076–1085.[PubMed][Google Scholar]
  • 29. Dolfi SC, Chan LL, Qiu J, Tedeschi PM, Bertino JR, Hirshfield KM, Oltvai ZN, Vazquez AThe metabolic demands of cancer cells are coupled to their size and protein synthesis rates. Cancer &amp; metabolism. 2013;1(1):20.[Google Scholar]
  • 30. Tedeschi PM, Markert EK, Gounder M, Lin H, Dvorzhinski D, Dolfi SC, Chan LL, Qiu J, DiPaola RS, Hirshfield KM, Boros LG, Bertino JR, Oltvai ZN, Vazquez AContribution of serine, folate and glycine metabolism to the ATP, NADPH and purine requirements of cancer cells. Cell death &amp; disease. 2013;4:e877.[Google Scholar]
  • 31. Xu J, Does MD, Gore JCQuantitative characterization of tissue microstructure with temporal diffusion spectroscopy. Journal of magnetic resonance. 2009;200(2):189–197.[Google Scholar]
  • 32. Ianus A, Siow B, Drobnjak I, Zhang H, Alexander DCGaussian phase distribution approximations for oscillating gradient spin echo diffusion MRI. Journal of magnetic resonance. 2013;227:25–34.[PubMed][Google Scholar]
  • 33. Stepisnik JTime-Dependent Self-Diffusion by Nmr Spin-Echo. Physica B. 1993;183(4):343–350.[PubMed][Google Scholar]
  • 34. Li H, Gore JC, Xu JFast and robust measurement of microstructural dimensions using temporal diffusion spectroscopy. Journal of magnetic resonance. 2014;242:4–9.[Google Scholar]
  • 35. Xu J, Li H, Harkins KD, Jiang X, Xie J, Kang H, Does MD, Gore JCMapping mean axon diameter and axonal volume fraction by MRI using temporal diffusion spectroscopy. NeuroImage. 2014;103C:10–19.[Google Scholar]
  • 36. Novikov DS, Fieremans E, Jensen JH, Helpern JACharacterizing microstructure of living tissues with time-dependent diffusion. ArXiv e-prints. 12102012[PubMed][Google Scholar]
  • 37. Gore JC, Xu JZ, Colvin DC, Yankeelov TE, Parsons EC, Does MDCharacterization of tissue structure at varying length scales using temporal diffusion spectroscopy. NMR in biomedicine. 2010;23(7):745–756.[Google Scholar]
  • 38. Selvam S, Thomas PB, Gukasyan HJ, Yu AS, Stevenson D, Trousdale MD, Mircheff AK, Schechter JE, Smith RE, Yiu SCTransepithelial bioelectrical properties of rabbit acinar cell monolayers on polyester membrane scaffolds. American journal of physiology Cell physiology. 2007;293(4):C1412–1419.[PubMed][Google Scholar]
  • 39. Pantanowitz L, Sinard JH, Henricks WH, Fatheree LA, Carter AB, Contis L, Beckwith BA, Evans AJ, Otis CN, Lal A, Parwani AVValidating Whole Slide Imaging for Diagnostic Purposes in Pathology Guideline from the College of American Pathologists Pathology and Laboratory Quality Center. Arch Pathol Lab Med. 2013;137(12):1710–1722.[PubMed][Google Scholar]
  • 40. Semmineh NB, Xu J, Boxerman JL, Delaney GW, Cleary PW, Gore JC, Quarles CCAn efficient computational approach to characterize DSC-MRI signals arising from three-dimensional heterogeneous tissue structures. PloS one. 2014;9(1):e84764.[Google Scholar]
  • 41. Conover WJ Practical nonparametric statistics. viii. New York: Wiley; 1999. p. 584. [PubMed][Google Scholar]
  • 42. Yoshikawa MI, Ohsumi S, Sugata S, Kataoka M, Takashima S, Mochizuki T, Ikura H, Imai YRelation between cancer cellularity and apparent diffusion coefficient values using diffusion-weighted magnetic resonance imaging in breast cancer. Radiat Med. 2008;26(4):222–226.[PubMed][Google Scholar]
  • 43. Squillaci E, Manenti G, Cova M, Di Roma M, Miano R, Palmieri G, Simonetti GCorrelation of diffusion-weighted MR imaging with cellularity of renal tumours. Anticancer research. 2004;24(6):4175–4179.[PubMed][Google Scholar]
  • 44. Panagiotaki E, Chan RW, Dikaios N, Ahmed HU, O’Callaghan J, Freeman A, Atkinson D, Punwani S, Hawkes DJ, Alexander DCMicrostructural characterization of normal and malignant human prostate tissue with vascular, extracellular, and restricted diffusion for cytometry in tumours magnetic resonance imaging. Investigative radiology. 2015;50(4):218–227.[PubMed][Google Scholar]
  • 45. Li H, Jiang X, Xie J, Gore JC, Xu JImpact of transcytolemmal water exchange on estimates of tissue microstructural properties derived from diffusion MRI. Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine/Society of Magnetic Resonance in Medicine. 2016[Google Scholar]
  • 46. Drobnjak I, Zhang H, Ianus A, Kaden E, Alexander DCPGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study. Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine/Society of Magnetic Resonance in Medicine. 2016;75(2):688–700.[Google Scholar]
  • 47. Colvin DC, Loveless ME, Does MD, Yue Z, Yankeelov TE, Gore JCEarlier detection of tumor treatment response using magnetic resonance diffusion imaging with oscillating gradients. Magnetic resonance imaging. 2011;29(3):315–323.[Google Scholar]
  • 48. Xu J, Li K, Smith RA, Waterton JC, Zhao P, Chen H, Does MD, Manning HC, Gore JCCharacterizing tumor response to chemotherapy at various length scales using temporal diffusion spectroscopy. PloS one. 2012;7(7):e41714.[Google Scholar]
  • 49. Xu JZ, Xie JP, Jourquin J, Colvin DC, Does MD, Quaranta V, Gore JCInfluence of Cell Cycle Phase on Apparent Diffusion Coefficient in Synchronized Cells Detected Using Temporal Diffusion Spectroscopy. Magnet Reson Med. 2011;65(4):920–926.[Google Scholar]
  • 50. Quirk JD, Bretthorst GL, Duong TQ, Snyder AZ, Springer CS, Ackerman JJH, Neil JJEquilibrium water exchange between the intra- and extracellular spaces of mammalian brain. Magnet Reson Med. 2003;50(3):493–499.[PubMed][Google Scholar]
  • 51. Zhao L, Kroenke CD, Song J, Piwnica-Worms D, Ackerman JJ, Neil JJIntracellular water-specific MR of microbead-adherent cells: the HeLa cell intracellular water exchange lifetime. NMR in biomedicine. 2008;21(2):159–164.[Google Scholar]
  • 52. Bailey C, Giles A, Czarnota GJ, Stanisz GJDetection of apoptotic cell death in vitro in the presence of Gd-DTPA-BMA. Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine/Society of Magnetic Resonance in Medicine. 2009;62(1):46–55.[PubMed][Google Scholar]
  • 53. Karger J, Pfeifer H, Heink WPrinciples and application of self-diffusion measurements by nuclear magnetic resonance. Advanced Magnetic Resonance. 1988;12:1–89.[PubMed][Google Scholar]
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