Intratumor mapping of intracellular water lifetime: metabolic images of breast cancer?

Shutter-speed pharmacokinetic analysis of dynamic-contrast-enhanced (DCE)-MRI data allows evaluation of equilibrium inter-compartmental water interchange kinetics. The process measured here - transcytolemmal water exchange - is characterized by the mean intracellular water molecule lifetime (τi). The τi biomarker is a true intensive property not accessible by any formulation of the tracer pharmacokinetic paradigm, which inherently assumes it is effectively zero when applied to DCE-MRI. We present population-averaged in vivo human breast whole tumor τi changes induced by therapy, along with those of other pharmacokinetic parameters. In responding patients, the DCE parameters change significantly after only one neoadjuvant chemotherapy cycle: while K(trans) (measuring mostly contrast agent (CA) extravasation) and kep (CA intravasation rate constant) decrease, τi increases. However, high-resolution, (1 mm)(2), parametric maps exhibit significant intratumor heterogeneity, which is lost by averaging. A typical 400 ms τi value means a trans-membrane water cycling flux of 10(13) H2O molecules s(-1)/cell for a 12 µm diameter cell. Analyses of intratumor variations (and therapy-induced changes) of τi in combination with concomitant changes of ve (extracellular volume fraction) indicate that the former are dominated by alterations of the equilibrium cell membrane water permeability coefficient, PW, not of cell size. These can be interpreted in light of literature results showing that τi changes are dominated by a PW (active) component that reciprocally reflects the membrane driving P-type ATPase ion pump turnover. For mammalian cells, this is the Na(+), K(+)-ATPase pump. These results promise the potential to discriminate metabolic and microenvironmental states of regions within tumors in vivo, and their changes with therapy.

INTRODUCTION

Tumor heterogeneity

Cell type and metabolic heterogeneity are crucial tissue characteristics. For example, there is much current interest in intratumor phylogenetic diversity. Its metabolic consequences are likely of great significance in therapy resistance or tolerance (1–6). This heterogeneity presents a challenge to blood tests, point biopsies, and ex vivo tissue homogenization, and puts a premium on in vivo assessment with the highest possible spatial resolution and on an individual-by-individual basis (7). The most feasible current methods of human metabolic imaging, 18 F positron emission tomography (8) and hyperpolarized 13C magnetic resonance spectroscopic imaging (9), are extremely informative, but generally have insufficient resolution (typically 5 and 7 mm, respectively) to clinically assay intratumor heterogeneity, and are costly. In contrast, water hydrogen proton (1H2O) MRI affords millimeter or sub-millimeter spatial resolution in human studies, uses no ionizing radiation, is minimally invasive, and is relatively inexpensive. Though millimeter or sub-millimeter does not match the resolution of histopathology microscopy, it detects considerable intratumor heterogeneity. Conventionally, however, 1H2O MRI is thought to provide only anatomical/vascular (and sometimes tissue functional) information. Fortunately, a new opportunity is presenting itself. It arises from the ability of MR to measure intercompartmental water molecule exchange kinetics. This study investigates the implications of the heterogeneity of such trans-cytolemmal kinetics within malignant human breast tumors before and after neoadjuvant chemotherapy (NACT).

BACKGROUND

Mean intracellular water molecule lifetime (τi)

The kinetics of the equilibrium (steady-state) exchange of water molecules across cell membranes have been studied by isotope labeling techniques for almost 60 years (reviewed in (10)) and by NMR methods for over 40 years (reviewed in (11–13). For a ‘well-mixed’ cytoplasm, the kinetics can be expressed in Equation [1]:where τi is the mean lifetime of a water molecule inside the cell, PW the cell membrane water permeability coefficient, and (A/V) the claustrophobia ratio (A is the individual cell surface area and V the individual cell volume) (14). The NMR community tends to report τi values (11–13) while the isotope community gives PW values: PW is often labeled Pd, the diffusive permeability (10). (We note that, even though they have the same dimensions (distance/time), PW [≡ Pd] is not the same as Pf, the water permeability coefficient in the presence of a transmural osmotic gradient, which causes net trans-membrane water transport (‘flow’) simultaneous with the much faster exchange (15–17).) Using Equation [1], one finds published PW and τi values to be in general agreement (13). The τi reciprocal, τi−1, is the unidirectional first-order rate constant, kio, for equilibrium water efflux from the cell – there is no nettransport (18). Values of τi−1 span four orders of magnitude – the extremes range from 10−2 s−1 for Xenopus oocytes to 102 s−1 for erythrocytes (11–13,19). For virtually all other cells, however, τi values are hundreds of milliseconds and the ‘well-mixed’ approximation is quite good (20). For only the very largest, e.g. the Xenopus oocyte (1 mm diameter), does this condition just begin to fail (19).

Equation [1] can be approximated with Equation [3]:where C is a constant shape factor and d the cell diameter. If the cell is spherically shaped, C = 6 (if the cell shape is well approximated as a right cylinder, C = 4). The quantity d is a one-dimensional (1D) measure of cell size.

There has been some recent concern (21) that interpretation of literature data on the blood wash-out following bolus injections of isotopically labeled water implies cerebral cortical τi ≥ 30 s. This is almost two orders of magnitude greater than values generally found (10–13). Taking a typical value of PW = 1.4 × 10−4 cm s−1 (10), a τi of 30 s in Equation [3] yields a d value of 250 µm: clearly much larger than the average cell (6). A simple tracer intravasation interpretation of the same blood wash-out data yields (22) a mean lifetime for extravascular water (τexv) of 21 s – in good agreement with the blood capillary water permeability coefficient from isotopically labeled water experiments. Seemingly, τexv has been mis-assigned as τi in (21).

Active trans-membrane water cycling

The equilibrium water exchange process has been conceived as resulting from passive molecular mechanisms: simple diffusion across the lipid bilayer, passage through aquaporin membrane protein channels, leakage through membrane transporters, etc. (23–25). Changes in d (or C) – cellular swelling or shrinking (edema) – will alter τi−1. However, the rate constant for d change is at least an order of magnitude smaller than τi−1 (kio) itself (15,17). Any τi−1 changes not due to d (or C) alterations must be due to changes in PW, which has always been thought of as a passive cell membrane property (PW(passive)). However, NMR studies have recently revealed an active component (PW(active)) much larger than the passive contribution (17). This is due to active trans-membrane water cycling that accompanies active trans-membrane osmolyte cycling, which is paced by the driving cell membrane P-type ATPase ion pump (17). For mammalian cells, this is the Na+,K+-ATPase, NKA (17,26–28). The existence of this water cycling is significant.

NMR principles

The classic NMR measurements are mostly of homogeneous cell suspensions. The presence of an extracellular paramagnetic contrast agent (CA) increases the intrinsic longitudinal relaxation rate constant R1o (≡ (T1o)−1) of the outside water proton signal (1H2Oo). Though the term was introduced only in 1999 (29), this approach increases the longitudinal ‘shutter-speed,’ т1−1 (≡ | R1o − R1i | ), sufficiently that the water exchange NMR system is moved out of the fast-exchange-limit (FXL) condition (R1i is the intrinsic intracellular relaxation rate constant). A sufficient outside CA concentration, [CAo], allows the NMR system to reach the slow-exchange-regime (SXR) condition. This is characterized by non-mono-exponential longitudinal magnetization recovery, but is distinct from the slow-exchange-limit and no-exchange-limit conditions (13,17,22,29,30). It is quite common to achieve the SXR with cell suspensions (11–13,17,22). However, if the [CAo] value is only modest, and the system reaches only the fast-exchange-regime (FXR) condition, then τi−1 measurement requires т1−1 variation (by varying [CAo]) (17,22,29–31). The FXR condition features apparent mono-exponential longitudinal recovery, i.e., the measured R1 is single valued, but has a non-linear [CAo] dependence. In the FXL condition, this dependence is linear (13,17,22,29,30). (Sometimes, transverse 1H2O relaxation is employed for cell suspensions (11,12)).

Dynamic-contrast-enhanced (DCE)-MRI

The spatial encoding of 1H2O in MRI offers the possibility of measuring, and mapping, τi values in human biological tissues in vivo. A stepped CA infusion producing incremental plasma and interstitial CA steady-state levels works well in animal models (29), but is impractical for human use. However, in the common clinical DCE-MRI approach, serial T1-weighted 1H2O images are obtained before, during, and after a bolus CA injection. The time-course of the CA bolus passage through the field of view is measured. The shutter-speed concept can be incorporated into the pharmacokinetic analysis of the time-course. This differs from the tracer pharmacokinetic paradigm, which is based on the fact that compartmentalization is not encoded in the tracer signal: it does not distinguish compartments entered by tracer. In DCE-MRI, CA compartmentalization is intrinsic to the 1H2O signal, which continuously tracks the amounts of H2O and CA in each compartment. Thus, imposition of a classic tracer analysis on DCE-MRI data joins these contradictory postulates about CA compartmentalization, and the only reconciliation is the inherent and incorrect assumption that the NMR system is always in the FXL condition, i.e., that τi is effectively zero. Thus, besides systematically distorting the values of other pharmacokinetic parameters, this renders τi−1 inaccessible. For a recent detailed overview, see (30). Immediately after a bolus intravenous (IV) injection, in almost all tissues CA transiently extravasates and NMR systems transiently depart the FXL for the FXR condition. There is no evidence that, with CA doses approved for human subjects, any system ever reaches the SXR condition (13,30). However, the interstitial CA concentration, [CAo] (and thus т1−1), value varies naturally – increasing and decreasing during the DCE time-course.

Using the shutter-speed pharmacokinetic paradigm (SSP), we (30,32–40) and others (41–45) have presented high-resolution, pixel-by-pixel, τi maps. Importantly, the τi magnitudes in the maps, and averaged over regions of interest (ROIs), are in general agreement with those from the many, precise NMR spectroscopic cell suspension measurements (11–13). This indicates that in vivo τi accuracy is reasonable.

Let us consider fundamental aspects of the DCE pharmacokinetic parameters as biomarkers. The Ktrans quantity, mainly a rate constant for capillary CA extravasation/tissue arrival, is elaborated in Equation [4]:kep is the first-order rate constant for CA intravasation, ve the CA distribution volume (mainly the extracellular, extravascular volume fraction), kpe the rate constant for CA extravasation, vp the blood plasma volume fraction, PCA the capillary wall CA permeability coefficient, and S the total blood capillary surface area (13,18,30,34,35,46). The ve, vp, and S magnitudes depend on the extent of voxel or ROI cell density (for ve) or capillary density (for vp or S) magnitudes. Thus, though the Ktrans, ve, and vp biomarkers are formally intensive quantities, their values reflect the numbers of cells or capillaries. The τi parameter, on the other hand, is a true intensive property. For spherical cells, Equation [3] yields τi = 0.17(d/PW), where d and PW represent, respectively, the mean voxel or ROI cell diameter and cytolemmal water permeability coefficient. The τi magnitude does not depend on the extent of the voxel or ROI cell density (ρ) value: τi is independent of ve, or the intracellular volume fraction, vi (≈(1 – ve)). This is an important, and novel, characteristic for an imaging biomarker.

EXPERIMENTAL

Subjects

We report on a cohort of 11 consecutive women undergoing NACT for locally advanced breast cancer diagnosed by core needle biopsy. The six-cycle therapeutic course was TP0–[NACT1]–TP1–[NACT2]–[NACT3]–TP2–[NACT4]–[NACT5]–[NACT6]–TP3, where TP is therapy point. Each three-week cycle comprised a single IV infusion of a drug cocktail. As per standard care, surgeries (seven mastectomies, four lumpectomies) followed TP3 – after 18 weeks of therapy. Pathology analyses of the surgical specimens are described below. The subjects underwent DCE-MRI studies at TP0, TP1, TP2, and TP3. In each case, DCE parameters were spatially averaged and/or computed pixel by pixel, and the results compared with pathology findings.

Two representative cases were selected for high-resolution parametric mapping and in-depth deductive analyses. In each of these, the tumor was a grade 2 invasive ductal carcinoma (IDC) and the patient was HER2 (human epidermal growth factor receptor 2) positive and BRCA1/BRCA2 mutation negative. One was determined a non-complete responder by pathology (non-pCR). (She is estrogen (ER) and progesterone (PR) receptor negative but has a family history of breast cancer.) Her NACT comprised a trastuzumab (monoclonal antibody interfering with HER2/neu receptor), docetaxel (anti-mitotic interfering with microtubules), and carboplatin (interferes with DNA repair) cocktail for each cycle. The other was determined a complete responder (pCR). (She is ER (100%) and PR (10%, focal) positive.) Her NACT comprised a trastuzumab and paclitaxel (anti-mitotic interfering with microtubules) cocktail for the first three cycles. Six weeks after our TP1 study of the pCR subject (i.e. after three NACT cycles), her therapy was switched to a cyclophosphamide (alkylating DNA interference) and Adriamycin (DNA intercalating) cocktail for the last three cycles.

DCE-MRI

The protocol was approved by the local Institutional Review Board. With informed consent, the patients participated in this ongoing MRI research study, which played no role in their clinical management. We have reported extensive details on DCE-MRI data acquisition from the breast (13,18,45,46) and prostate (30,47). Here, axial bilateral DCE-MRI images with fat saturation and full breast coverage were acquired with a 3D gradient echo-based time-resolved angiography with stochastic trajectories sequence (45) using a Siemens 3 T instrument. DCE-MRI acquisition parameters included 10o flip angle, 2.9/6.2 ms TE/TR, a parallel imaging acceleration factor of two, (30–34 cm)2 FOV, (320)2 matrix size, and nominal 1.4 mm slice thickness. The nominal in-plane resolution was (1.1 mm)2. This yielded a nominal 1.7 μL voxel. The total acquisition time was ∼10 min for 32–34 image volume sets with 18–20 s temporal resolution. The CA Gd(HP-DO3A) (ProHance) IV injection – 0.1 mmol kg−1 (the clinical single dose) at 2 mL s−1 – was carried out following acquisition of two baseline image volumes. A population-averaged arterial input function was obtained from axillary arteries (13,18,46). We used the FXR-allowed SSP version – detailed in (30) – for analyses of spatially averaged and pixel-by-pixel DCE-MRI time-course data. These were subjected to both tracer and shutter-speed pharmacokinetic analyses to extract the Ktrans, ve, kep (= Ktrans/ve), and τi (SSP only) DCE parameters.

Our focus is mostly on high-resolution parametric maps. However, there is some spatial averaging. These tumors are sufficiently heterogeneous that the averaging method must be specified. The (a) ‘whole tumor’ mean parameter values were calculated as the weighted (by ROI pixel number) averages of the (b) ‘single image slice-averaged’ ROI values from the image planes covering the entire tumor. For image slice-averaged results, the DCE-MRI time-courses from all pixels in the chosen tumor image slice are averaged before pharmacokinetic analysis. For (c) ‘image slice pixel-averaged’ data, the individual pixel time-courses are analyzed and then the resulting parameters averaged.

Parameter precision from Monte Carlo simulations

For the pCR subject selected for in-depth analyses, the precision of fitted DCE parameters (τi and Ktrans) was estimated using a Monte Carlo approach detailed previously (48). The DCE-MRI time-courses for each tumor pixel in the chosen image slice, obtained at both TP0 and at TP1, were analyzed. Six fittings of each voxel DCE-MRI time-course were made, starting with randomly different initial sets of parameter values spanning broad ranges. The standard deviations (SDs) of the returned parameter values were calculated.

Histology

The response to NACT for each patient was determined by pathology analysis of post-therapy surgical specimens (after TP3) and comparison with pre-therapy biopsy specimens (before TP0). This comprised the determination of the residual cancer burden (RCB) and the relative change in tumor cell density using published methods (49,50). These analyses revealed that three patients were pCR – no cancer cells found in resection specimens – while the other eight were non-pCR – reduced cancer cell density in resection specimens compared with biopsy specimens. For the non-pCR case selected for in-depth analysis, a whole-mount slide of a slice of a biopsy core obtained pre-therapy (before TP0) was used to estimate the extent of necrosis and the cell densities in regions of the parametric tumor rim and tumor core. The biopsy core was obtained with a 14 gauge needle (1.6 mm ID), inserted from medial to lateral, and the hematoxylin and eosin (H&E)-stained slide was examined by microscopy at both low and high power (200×).

Statistical analyses

Tumor ROIs were drawn by experienced radiologists, who also measured the largest 1D tumor size according to the RECIST (Response Evaluation Criteria in Solid Tumors Group) (51) guideline. The results from pathology analyses were correlated with the MRI metrics using the ULR (univariate logistic regression) analysis in order to identify imaging biomarkers for early prediction of response and/or accurate assessment of residual disease following NACT.

RESULTS

Human breast cancer and therapy

We have presented many DCE time-courses of breast (13,18,46) and prostate (30,47) cancer data. Figure 1 displays whole breast axial DCE image slices obtained during CA passage for two subjects with IDC representative of the population here – one found a non-pCR (Fig. 1(a), (c); left breast) and one a pCR (Fig. 1(b), (d); right breast). The scale bars are 2 cm. The Figure 1(a), (b) images were obtained at TP0 – before NACT; the Figure 1(c), (d) images were obtained at TP1 – after one NACT cycle. Since three weeks separate the DCE-MRI acquisitions, the image slices cannot be perfectly registered. The image slice displayed for TP1 represents a best estimate for equivalence to the image slice for TP0. Enhancing tumor regions are clearly hyperintense in these T1-weighted images. As examples, the red borders in Figure 1(a), (c), demarcate the radiologist-selected tumor ROIs in these image planes.

Figure 1

Axial breast T1-weighted images, obtained during CA bolus passage, from two representative subjects in the population. (a) The left breast, before therapy (TP0), of one of eight subjects deemed a non-pCR after 18 weeks of NACT. (c) The same subject after 3 weeks of NACT (TP1). (b), (d) Right breast images of one of three subjects declared pCR, obtained at TP0 and TP1, respectively. Each patient had grade 2 IDC breast cancer. The radiographic tumor outlines are marked in red in (a) and (c). The scale bars are 2 cm.

Figure 2 shows 12 zoomed pixel-by-pixel SSP parametric maps of the Figure 1 tumors, six from each subject. The upper six ((a)–(f)) are from the Figure 1(a), (c) non-pCR and the lower six ((g)–(l)) are from the Figure 1(b), (d) pCR case. The top row of maps ((a)–(c), (g)–(i)) for each patient was obtained at TP0 – before NACT initiation. The bottom row ((d)–(f), (j)–(l)) was obtained at TP1 – after one NACT cycle; three weeks. Besides the τi maps, the other pharmacokinetic parameters are Ktrans and ve. The color scales (Ktrans in min−1; τi in s) are given; ve is dimensionless.

Figure 2

Zoomed shutter-speed DCE-MRI parametric maps of the two tumors shown in Figure 1. (a)–(f) Subject non-pCR; (g)–(l) pCR. (a)–(c), (g)–(i) were obtained pre-therapy (TP0), and (d)–(f), (j)–(l) 3 weeks into (TP1) the 18 week NACT course. The biomarkers Ktrans (a), (d), (g), (j), ve (b), (e), (h), (k), and τi (c), (f), (i), (l) measure, respectively, CA extravasation kinetics, extracellular volume fraction, and mean intracellular water lifetime, and exhibit intratumor heterogeneity. Analyses of τi and ve relationships for 21 pairs of seven different ROIs within these maps (two outlined in yellow in (c)) indicate that the τi maps reflect metabolic activity: the smaller τi, the greater the NKA turnover. Note the τi scale change.

We briefly divert to spatial- and population-averaged results. Figure 3 is a column graph showing the early therapeutic responses of whole tumor-averaged parameter values, further averaged over the pCR (black bars) and non-pCR (gray bars) sub-populations. The error bars reflect the considerable inter- and intratumor (Fig. 2) heterogeneity averaged. The parameters are RECIST, Ktrans(tracer), Ktrans(SSP), kep(tracer), kep(SSP), and τi. The vertical axis measures the percentage change in the biomarker after the first NACT cycle, i.e. in the three weeks between TP0 and TP1. The bar color (pCR versus non-pCR), however, is determined only after completion of the entire NACT therapeutic course (18 weeks), surgery, and pathology analyses. Though the mean tumor size (RECIST) decreased only slightly after three weeks, the DCE biomarkers showed larger changes. Interestingly, the SSP Ktrans and kep parameters decreased for the pCR sub-population, while τi increased. Overall, the ULR analysis found that the percentage changes in tumor mean Ktrans (tracer and SSP), kep (tracer and SSP), and pixel τi histogram median after the first NACT cycle (at TP1 relative to TP0) were excellent discriminators of pCRs from non-pCRs, each with the ULR c statistic value of 1.0 (meaning complete separation), while the early RECIST percentage change was a poor predictor with c = 0.60. (The ve parameter has c values less than unity.) In addition, the absolute values of TP1 tumor mean Ktrans(SSP) and kep (tracer and SSP) were also effective (c = 1.0) early discriminators (not shown). After only one NACT cycle, changes in the tumor-averaged shutter-speed DCE biomarkers Ktrans, kep, and τi are excellent predictors of the therapeutic outcome to be found after NACT completion. This is very encouraging. We have published a preliminary report with more results (40), and plan a full paper on these aspects. The tumor-averaged Ktrans(SSP) and τi values at TP3 significantly correlate with the RCB magnitude found by pathology analyses.

Figure 3

Sub-population-averaged whole tumor biomarker values. The vertical axis measures the percentage change after the first three weeks of therapy (between time point TP0 and time point TP1). The bar colors represent the sub-populations after 18 weeks of therapy, discriminated by pathology analysis: black, pCR (n = 3); gray, non-pCR (n = 8). The RECIST parameter is a radiographic tumor size measure; the others are DCE-MRI kinetic parameters from tracer or SSP analyses: Ktrans (mainly CA extravasation), kep (CA intravasation), and τi (mean intracellular water lifetime). The change in DCE-MRI biomarkers after three weeks, particularly those from SSP – including τi, are excellent predictors of therapeutic outcome after 18 weeks. For the responders, τi increases, signifying a therapeutically induced decrease in metabolic activity.

However, the significant intra- and intertumor heterogeneity (1–6) described above seriously calls for individualized tumor assessment (7). For the remainder of this paper, we return our focus to the intratumor parametric maps of the two representative Figure 1, 2 case studies. These allow in-depth deductive analyses of τi interpretation. In these, the subjects serve as their own controls. Figure 4 shows τi (ordinate), Ktrans (abscissa) scatter plots of the 228 tumor pixels from Figures 2(g), (i) (0.38 mL ROI) (a) and the 142 tumor pixels from 2(j), (l) (0.24 mL ROI) (b). These are for the representative pCR patient. The τi values in NMR spectroscopic cell suspension studies and in ROIs can be determined with precisions better than 5% (17) and 10% (30), respectively. However, single voxel DCE-MRI data have greater relative noise, which could diminish pixel τi precision. Figure 4(a), (b) appraises this for the Figure 2(i), (l) pixels, respectively. Figure 4(a), (b) shows the mean parameter values (black circles) returned from fittings of each pixel time-course. The gray error bars show the SDs for the six fittings from randomly chosen initial parameter value sets (48). All error bars are present: many are smaller than the circles. In these cases, the τi precision seems comparable to, or better than, that of cell suspension studies. But some fitting uncertainties are larger. Inspection of Figure 4(a) shows, however, that these occur only in regions where Ktrans is relatively small. In these cases, [CRo] and thus the shutter speed (т1−1) does not become very large for very long, and the system does not depart the FXL for the FXR condition very extensively and/or for a very long duration (13,30,32). Interestingly, these greater uncertainties occur for both small and large τi values. This indicates that τi precision is not particularly dependent on τi magnitude (the error bar is relatively independent of the mean). It implies that the τi accuracy is relatively independent of τi precision. This is also found for ROI data (30).

Figure 4

Pixel τi (ordinate), Ktrans (abscissa) scatter plots of the Figure 1(b), (d) pCR tumor (a) pre- (Fig. 2(g), (i)) and (b) post- (Fig. 2(j), (l)) therapy. These show the mean τi, Ktrans values (black points) returned from six fittings of single voxel DCE-MRI time-courses with randomly different initial parameter sets. The gray error bars show the SDs of the fittings, and thus reflect parameter precision. All error bars are present: many are smaller than the points. Poorer τi precision occurs for pixels in tumor regions with small Ktrans values – in agreement with theory. There is a substantial Ktrans decrease and an overall τi increase after therapy.

The situation in Figure 4(b) (pCR, TP1; Figure 2(j)) is different from that in Figure 4(a). As shown in Figure 3, the large Ktrans decrease is good news for the pCR patient. (The tumor image slice-averaged Ktrans decreases from 0.19 min−1 at TP0 (Fig. 2(g)) to 0.04 min−1 at TP1 (Fig. 2(j)) – i.e. by 79%.) However, the greatly diminished Ktrans provides a difficult scenario for precise τi determinations. The error bars reflect this. Nonetheless, one can discern that, on the whole, τi values are larger than in Figure 4(a). (The tumor image slice pixel-averaged τi goes from 0.32 s at TP0 (Fig. 4(a)) to 0.39 s at TP1 (Fig. 4(b)) – a 22% increase.) This result reinforces the notion that the τi magnitude itself does not decrease with Ktrans: mostly, the precision of its determination becomes poorer. When clinically indicated, this precision can be considerably improved by moving up to the approved triple CA dose.

A 2D scatter plot is an effective way to take advantage of two responsive biomarkers (52). The slight negative spatial τi, Ktrans correlation apparent to the eye in the Figure 2(g), (i) parametric maps can also be barely discerned in Figure 4(a). The Pearson correlation coefficient is −0.23. The substantial decrease in Ktrans values after one NACT cycle (TP0 (a), TP1 (b)) is quite obvious. It is also clear from Figure 4(b) that the τi and Ktrans magnitudes are independent: they are not numerically correlated by the analysis. As we have seen, the pCR tumor- and population-averaged τi increases after therapy (Fig. 3). From Figures 2(i), (l) and 4(a), (b), we can detect an overall increase in τi after NACT. (The whole tumor-averaged τi increases from 0.27 s to 0.41 s – i.e. by 52%.) Figure 2(l) suggests that this is localized mainly in the tumor core. From the τi perspective, we can see from Figure 3 (based on whole tumor averages) that the result for the patient of Figure 2(i), (l) represents the most conservative of the three pCR cases. Importantly, there are no significant ve differences between core and rim after therapy (Fig. 2(k)). As we will see, the tumor core τi increase by therapy is due to a PW decrease.

Parameter heterogeneity, relationships, and therapy responses

Though the tumors appear relatively homogeneous in Figure 1, the SSP parametric maps exhibit significant intratumor heterogeneity that appears anatomic in nature. For example, the TP0 Ktrans maps of each tumor display elevated values in the tumor rim relative to the core. In Figure 2(a), (g), the Ktrans variation exceeds a factor of 10. This pattern is common. It is observed in malignant human tumors – breast (37,46), osteosarcoma (35), head and neck (43), and soft tissue sarcoma (53), in spontaneous murine breast tumors (39), and in implanted rodent cerebral gliosarcoma (32), RIF-1 (33) and prostate (38) tumors. However, it is by no means universal: tumors with bright Ktrans cores (or multiple cores) have been reported for malignant human breast (18,34,35,41,42), head and neck (44), and prostate (47) tumors, and in implanted rat glioma (54). The observation of this diversity is very promising for individualized imaging.

Furthermore, there are often spatial correlations between the imaging biomarkers. In the Figure 2 Ktrans/τi pairs (especially (a)/(c) and (j)/(l), less so for (d)/(f) and (g)/(i)), regions with relatively elevated Ktrans values generally have relatively smaller τi values, and vice versa. (The non-pCR core τi is quite large, 1 s (Fig. 2(c)).) This is also often observed in other human malignant tumors – breast (34,35,37), osteosarcoma (35), head and neck (43,44), and prostate (36) – and in spontaneous murine breast tumors (39). However, this negative correlation is not always the case: there are counter-examples in the human breast (41,42) and in implanted rodent gliosarcoma (32,55), RIF-1 (33), and prostate (38) tumors. Thus, the sign of the biomarker spatial correlation is independent of the intratumor heterogeneity spatial pattern.

For each Figure 2 patient, a comparison of a TP0 parametric map with that at TP1 shows the effect of the first NACT cycle. Figure 2(g), (j) reveals a significant Ktrans decrease after the first three weeks of therapy for the pCR subject, while there is little, if any, decrease for the non-pCR patient (Fig. 2(a), (d)). The Ktrans decrease for the pCR tumor is consistent with the results reported for essentially every antivascular cancer drug tested (56). Interestingly, the τi values increase (44% for the tumor image slice-average) for the pCR patient (Fig. 2(i), (l); note the more sensitive color scale), but not for the non-pCR individual (Fig. 2(c), (f)). Thus, there is a negative τi, Ktrans correlation in (therapy) time as well in space. Importantly, the τi increase and Ktrans decrease after 3 weeks of NACT predict very well that no RCB will be surgically found after 15 more weeks of therapy. This response is representative of the pCR tumor- and population-averaged results, and occurs usually before significant tumor size decrease (Fig. 3). This is also true for the Ktrans decrease caused by therapy on soft tissue sarcoma (53).

We also see τi increase/Ktrans decrease after a different therapy on a spontaneous murine breast tumor (39). It is important to note that the rather large tumor τi value (0.56 s, image slice average) in Figure 2(l) is obtained while ve is also very large, 0.87 (image slice average, Figure 2(k)). If ve is large, then vi (≈1 − ve) is small. This result reinforces the fact that, contrary to what one might intuit, the τi magnitude does not decrease with vi. This is because of its intensive nature.

Changes in τi reflect membrane permeability changes

For globular cells, Equation [3] gives τi−1 ≈ 6PW/d: PW is the membrane water permeability, d the cell diameter. For a spherical cell with a conservatively large d value (15 µm (6)), τi−1 = 4000PW (τi in s, PW in cm s−1). For a spherical cell with a typical PW value (1.4 × 10−4 cm s−1 (10)), τi−1 = 8.4/d (d in µm). Thus, τi−1 (kio) is linearly related to PW and linearly related to d−1, with different coefficients. Do observed τi variations reflect changes in PW, in d, or in both? In this paper, we compare relative (%) changes in τi−1 values within human breast tumors with the accompanying % d−1 changes, to show that PW dominates τi.

Let us inspect a τi variation in Figure 2. Consider the τi map of the non-pCR patient at TP0 (Fig. 2(c)). We choose an ROI representative of the annular tumor rim: we designate it RN0, for rim, non-pCR, at TP0. The average τi value for RN0 is 0.60 s. For a conservative ROI representative of the outer core, CN0, the τi value is 0.81 s (the inner core has even larger τi values). These ROIs are outlined with yellow borders in Figure 2(c). RN0 comprises 55 pixels (66 mm2; 94 μL), while CN0 comprises 43 pixels (52 mm2; 73 μL). The ratio {(τi[R])−1/(τi[C])−1} is 1.7/1.2 = 1.4: there is a 40% increase in kio for the rim over the core. Thus, the relationship {PW[R]/PW[C]}{(dR)−1/(dC)−1} = 1.4 must be satisfied. There is an infinite number of possibilities. If dC = 0.9dR, PW[R] = 1.6PW[C]; if dC = dR, PW[R] = 1.4PW[C] (the mean transcytolemmal water permeability is 40% larger in the rim); and if dC = 1.4dR (the mean cell diameter in the core is 40% larger than in the rim), PW[R] = PW[C].

If possible, it is extremely difficult (and invasive) to determine actual d values in vivo. However, one can evaluate their variations by combining DCE-MRI results with histology. We obtain and map ve values (e.g. Fig. 2(b)) and (1 − ve) ≈ vi ≡ ρV, where vi is the intracellular volume fraction, ρ the mean cell number density, and V the mean individual cell volume (Equation [1]). For spherical cells, the mean effective cell diameter d′ ∼ V1/3 ≈ {(1 − ve)/ρ}1/3. For the Figure 2(b) RN0 and CN0 ROIs (those marked in Fig. 2(c)), the ve[R] and ve[C] values are 0.38 and 0.73, respectively. Thus, {(1 − ve[R])/(1 − ve[C])}−1/3 = 2.3−1/3 = 0.76. The relationship {(d′R)−1/(d′C)−1}{(ρC)1/3/(ρR)1/3} = 0.76 must be satisfied.

A τi ratio measurement gives an experimental relationship between d and PW ratios. A ve ratio measurement gives an experimental relationship between d (taking d = d′) and ρ ratios. In the appendix, the Figure A1 3D plot shows the trace of all points that simultaneously satisfy both experimental relationships for the non-pCR tumor at TP0. If the ρC/ρR ratio is determined independently, one can evaluate whether τi changes are dominated by d changes or by PW changes, or whether both contribute significantly.

To do this, we examined an H&E histology slide of a slice of a biopsy core obtained 24 days before the non-pCR tumor was imaged at TP0. The whole mount slide was studied, and microscopic images made at two higher powers. We identified the biopsy core sections corresponding to the 8 mm thick tumor rim and the 5 mm radius tumor core seen in Figure 2(a)–(c). Five different tissue types were identified with predominantly (1) stromal cells, (2) adipocytes, (3) invasive carcinoma cells, (4) inflammation (usually lymphocytes), or (5) necrosis. These of course have different cell sizes (d) and densities (ρ) (6). We estimated the five tissue type area fractions in the tumor rim and tumor core. This tumor (before NACT) was not particularly necrotic – ∼15% in both the tumor rim and tumor core. The highest power (200×) H&E fields were used to determine cell densities representative of each tissue type. Thus, we calculated ρR as 416 × 103 and ρC as 256 × 103 cells mm−3. (These correspond to 706 × 103 and 434 × 103 cells/voxel in rim and core (1.7 μL voxels), respectively; 39 × 106 cells in RN0 and 19 × 106 cells in CN0.) This gives ρC/ρR = 0.6: the tumor core has 60% of the cell density of the tumor rim.

In Figure A1, the point with experimental ρC/ρR = 0.6 has coordinates dC = 0.9dR, and PW[R] = 1.6PW[C]. Even accounting for uncertainty in our cell density determination, Figure A1 shows that the mean dC and dR values are similar, and PW[R] is 40–75% larger than PW[C]: i.e., if anything, greater than the experimental τi−1 ratio. The conclusion is strong that the 40% increase in τi−1 measured for the rim over the core ROIs in non-pCR at TP0 (Fig. 2(c)) is dominated by a PW increase and not a d decrease. (This is one of the most conservative ROI pairs (very small τi−1 ratio) we could have chosen.) One may normally expect that it is cells in a tumor core that have an increased PW(passive) value (57), and this might be the case here as well. However, it is shown below that τi−1 is dominated by PW(active), and the PW[R] > PW[C] result for non-pCR at TP0 may constitute additional evidence that PW(active) > PW(passive). The tumor core cells could have increased PW(passive) but decreased PW(active), with a net PW decrease (or increased PW(active), as long as the rim cells have an even greater PW(active) increase).

What about τi variations in other ROIs? Besides RN0 and CN0 (Fig. 2(b), (c)), five other representative ROIs were chosen: RN1 and CN1 (Fig. 2(e), (f)), RC0 and CC0 (Fig. 2(h), (i)), and CC1 (Fig. 2(k), (l)) (in the ROI labels, the first character is R (rim) or C (core), the second character is N (non-pCR) or C (pCR), and the subscript is 0 (TP0) or 1 (TP1)). Taken two at a time, these seven ROIs afford 21(= 7!/(5!2!)) ROI pairs and thus 21 τi−1 and (1 − ve)−1/3 ratios. With analyses similar to the above, percentage τi−1 and d changes were estimated. (We did not separate the ρ ratio and d ratio factors. Since such ROIs average over at least 20 million cells of different types, sizes, and densities, these ratios are unlikely to deviate far from unity.) The results for 21 ROI pairs average to a 74% τi−1 increase accompanied by a 5% d decrease (not statistically different from zero). (Details are given in appendix Table A1.) This result is displayed in the Figure 5 column graph. It is very consistent with literature results also compiled and presented in Figure 5, which summarizes reports of experimentally induced τi changes that also have accompanying measurements allowing calculation or estimation of d changes. These span three model systems: two cell suspensions (17,31 and murine myocardium 58). (Details for these are also given in Table A1.) Cisplatin treatment induces an apoptotic state in acute myeloid leukemia (AML) cells and elevates τi−1 by almost 400% (31). However, the mean d decreases by only 9%. Switching the bubbling gas from N2 to O2 increases yeast τi−1 by 110%, but the mean d decreases by only 7% (17). For in vivo mouse myocardium, the normal τi−1 is 130% greater than in chronic hypertension (58), and yet the mean ex vivo cylindrical cardiomyocyte d is decreased by only 23% (58). It is important to note that two of these studies (31,58) included microscopy before and after the perturbation.

A1

Trans-membrane water exchange increases are disproportionately larger than cell size decreases

System	AML cells (n = 5)	Yeast cells (n = 6)	Murine myocardium in vivo/ex vivo (n = 17)	Human breast tumors in vivo (21 ROI pairs)
Smaller τi−1 (kio) (s−1) (larger τi, τi[L])	1.4 (±43%)a	1.5 (±6%)b	2.3 (±29%)c
Larger τi−1 (kio) (s−1) (smaller τi, τi[S])	6.8 (± 57%)d	3.1 (±3%)e	5.3 (±43%)f
τi−1 (kio) change	390% increase	110% increase	130% increase	74% increase (±37%)i
(dL’)−1 for smaller τi−1	1.0 (±10%)g	2.2 (±2%)g	0.038 (±6%)c,h (µm−1)
(dS’)−1 for larger τi−1	1.1 (±4%)g	2.4 (±2%)g	0.051 (±5%)f,h (µm−1)
(d’)−1 change	10% increase	9% increase	34% increase	5% increase (±22%)j
Reference	31	17	58	this work

Control cells.

N2 gasification.

L-NAME-treated mice, in vivo.

Cisplatin-treated cells.

O2 gasification.

Control mice, in vivo.

d’ = (pi)1/3.

Cylindrical diameter by microscopy on ex vivo fixed tissue.

Average for 21 ROI pairs in Figure 2 (see text).

Average {(dS′)−1/(dL′)−1}{ρL/ρS}1/3 for 21 ROI pairs in Figure 2 (ρ is cell number density); not statistically different from 0%.

Figure 5

Precedents comparing transmural water exchange kinetics increases with cell size decreases. The green bars represent percentage increases in the rate constant kio (τi−1), the red bars percentage decreases in mean cell diameter. Exchange sped up when AML cells were incubated with cisplatin (31), when yeast cells were switched from bubbling with N2 to O2 (17), and when hearts in chronically (induced) hypertensive mice were compared with control mice (58). In this work, 21 pairs of ROIs (in two human breast tumors pre- and post-therapy, Figure 2(a)–(l)) were compared, always taking the ROI with larger kio as the numerator, and the results averaged. (Details in Table 2.) The exchange kinetics increases are not dominated by cell size decreases.

The comparable nature of these model system results and our in vivo human breast tumor findings makes a compelling case that observed τi−1 variations are dominated by PW changes, not size changes. This is reinforced by the fact that, even though they are of similar (small) size, τi−1 is ∼4000% greater for the human erythrocyte (59) than for the yeast cell (17). It is very fortunate that nature exhibits this phenomenon.

DISCUSSION

As described above, the analysis of DCE-MRI time-course data with any formulation of the tracer pharmacokinetic paradigm (most common by far) is incorrect. It neglects the finite kinetics of the inter-compartmental water exchange equilibria that precede the rate limiting step of CA extravasation. This causes systematic changes in the DCE-MRI pharmacokinetic parameters, Ktrans and ve. In particular, spatially averaged Ktrans is disproportionately depressed in malignant tumors of the breast (13,18,34,35,46) and prostate (30,47). The SSP allows extremely high specificity in the detection of these cancers: specificity not possible with tracer analysis. This makes effective cancer detection (13,18,34,46,47) and therapy prediction (40,53) practical.

Here, however, we focus on the second benefit of the SSP, access to the water exchange kinetics themselves. This is not possible with the tracer paradigm, where water is not considered molecular but merely a continuum filling tissue compartmental spaces. The equilibrium trans-cytolemmal water exchange kinetics are measured by τi, the reciprocal of the unidirectional rate constant for water efflux, kio.

Changes in τi reflect changes in the driving membrane P-type ATPase ion pump turnover

The results above indicate that the intratumor τi variations observed in human breast cancer are dominated by PW differences. If they were dominated by d, the τi−1 (kio) percentage increases and d percentage decreases would be similar. Still, are the differences observed in PW(passive), in PW(active), or in both?

Almost all cells have a driving membrane P-type ATPase ion pump enzyme, which serves to generate transmural ion gradients and membrane potentials (26). For yeast cells, this is the H+-ATPase, Pma1 (17,26). For mammalian cells, it is NKA (26). The forward reaction catalyzed by NKA can be written as in Equation [5], where intracellular adenosine triphosphate (ATPi) is hydrolyzed to ADPi and Pi,extracellular potassium (Ko+) is transported into the cell, and intracellular sodium (Nai+) is expelled. Table 1 summarizes the literature on the dependence of equilibrium transcytolemmal water exchange kinetics (τi−1) on driving membrane P-type ATPase ion pump gene dosage, substrate concentration, and specific inhibitor concentration in yeast suspension, perfused rat heart, and erythrocyte suspension studies. Without exception, τi−1 increases with gene copy number and substrate concentration, and decreases with extracellular inhibitor concentration. (Ebselen and ouabain are specific inhibitors of Pma1 (17) and NKA (26), respectively.) This is strong evidence that τi−1 (kio) is dominated by PW(active), which in turn is driven by P-type ATPase ion pump turnover. The greater the turnover, the faster the exchange. All of these model systems were homeostatic for the Table 1 entries.

Table 1

τi-1 (kio) reflects turnover of driving membrane P-type ATPase ion pump

P-type ATPase ion pump	Yeast17	Cardiomyocyte28	Erythrocyte61
Gene dosage	↑↑
Substrate
ATPi	↑↑		↑↑
Ko+		↑↑
Specific inhibitor
Ebselen	↑↓
Ouabain		↑↓

↑↑ positively related; ↑↓ inversely related.

17Measured 17; 28measured 28; 61inferred 61.

Figure 6 presents a schematic diagram of the general molecular mechanism we have proposed 17 for active trans-membrane water cycling. The passive water exchange (PW(passive)) equilibrium is indicated at the top right. It involves simple water diffusion through the phospholipid bilayer, transport through aquaporin channels 60,61, and leakage through membrane protein transporters 25. Active trans-membrane water cycling (PW(active)), which can have three times the PW(passive) flux 17, almost certainly involves water co-transporting membrane symporters 24. In the diagram, active water efflux is pictured as passing through NKA, and influx through the sodium glucose co-transporter (SGLT 62), but this is only for the purpose of illustration. It is not yet known which symporter molecules dominate active water cycling: there are a number of candidates, SGLT certainly being one of them 24. By themselves, aquaporins catalyze only passive transmural water transport. However, to the extent to which they co-localize with substrate transporters, say K+ channels 60 or NKA 63, they may participate in active trans-membrane water cycling.

Figure 6

Schematic depiction of active trans-membrane water cycling (PW, cell membrane water permeability coefficient; C6H12O6, glucose; SGLT, sodium glucose co-transporter; NKA, Na+/K+-ATPase; KcsA, K+ channel). Water transport through NKA and SGLT is shown only for illustration. The principal transporters are not yet known.

Because it maintains the trans-membrane ion gradients that drive much secondary active transport and produce the membrane potential, one can argue that NKA is the most important enzyme in mammalian biology. Because of the particular, dual (‘vectorial’ and ‘scalar’ 64) characteristics of the reaction catalyzed by NKA (Equation [5]), measurements of its activity have always been adapted to the nature of the sample. For solubilized, purified enzyme or tissue homogenate preparations, one cannot measure the kinetics of (vectorial) ion transport. Thus, spectrophotometric 65 or radiolabeled (32P) assays 66 of the rate of ATP hydrolysis are used. On the other hand, for intact cells in culture or in tissue preparations, one cannot easily measure the kinetics of the (scalar) intracellular ATP hydrolysis caused by NKA activity. However for such samples, voltage clamp current, ion-selective (Na+/K+) microelectrode response, radioisotope (22Na+/24Na+/42 K+/86Rb+) uptake/release 67–70, or 23Na, 87Rb MR spectroscopic 71,72 methods can be used to measure NKA-driven trans-membrane ion transport kinetics. This is how it was learned that, when the concentrations of the other reactants and products have typical values, the intracellular Na+ concentration, [Nai+], is generally the rate-determining factor 71,73,74. It is also possible to measure [Nai+] using a fluorescent indicator 75. A breakthrough found that phospholipid vesicles reconstituted with purified NKA facilitated measurement of both ATP hydrolysis and ion transport 66. This allowed confirmation of the NKA reaction stoichiometry 66.

It is obvious that each of these methods is best suited to macroscopically homogeneous samples. None are particularly appropriate for use with normally heterogeneous tissue. (NKA distributions can be mapped histologically 76.) Except for the microelectrode approaches, these do not involve spatial encoding; and one cannot insert electrodes in all of the cells of a tissue. Furthermore, many of these methods directly measure only net NKA activity, not homeostatic NKA turnover. (An analogous problem arises measuring net versus steady-state water transport kinetics 15.) A 24Na+ study reveals the existence of an equilibrium transmural Na+ exchange process in the cardiomyocyte over an order of magnitude faster than net Na+ transport 69. However, the radioisotope approach has been generally abandoned for ∼20 years, and deemed too problematic for even tissue preparations 73. As far as we are aware, the NKA turnover has never been measured, let alone mapped, in a living animal or human subject. Therefore, τi−1 measurement offers the possibility of quantifying perhaps the most crucial ongoing cellular metabolic turnover. For a spherical cell with d = 12 µm, τi = 400 ms signifies active cycling of 7 × 1013 H2O molecules s−1/cell 17. If the stoichiometric flux ratio fluxNa+ = (10−3 to 10−2)fluxH2O 24 pertains, the Na+ flux is 1011–1012 Na+ ions s−1/cell. If τi maps are reciprocal NKA turnover maps, they represent high-resolution metabolic images.

We show that τi exhibits significant intratumor heterogeneity in human breast cancer in vivo. That the biomarker spatial correlations are never perfect and that counter-examples exist suggest that, when seen, these are not numerical co-variance artifacts resulting from the three parameter fittings of DCE-MRI data time-courses. They appear to be physiological correlations.

The synergism of two responsive imaging biomarkers can be very powerful. In this case, one reports on kinetic processes occurring outside cells: Ktrans measures mostly the microvascular CA extravasation/tissue arrival rate. The other (τi) measures metabolic fluxes inside cells. Since CA employs a para(endothelial)cellular pathway 77,78, it serves also as a surrogate for paracellular extravasation of plasma solutes with similar molecular sizes. Nutrients, particularly glucose 79, represent a crucial sub-class of these. Though glucose has specific transcellular transporters, when Ktrans is relatively large it is likely that additional paracellular glucose extravasation is also relatively large. When Ktrans is relatively large but τi is relatively small, as in the rims of both Figure 2 tumors before therapy, it may be signaling that greater nutrient delivery enables faster cell metabolism. The pre-therapy biopsy core for non-pCR showed clearly that the parametric rim seen in Figure 2(a)–(c) corresponds to a band with the greatest density of invasive carcinoma cells and inflammatory lymphocytes. Figure 2 suggests that NACT on the pCR tumor causes rim tissue to move from larger Ktrans/smaller τi to smaller Ktrans/smaller τi, and core tissue from smaller Ktrans/smaller τi to smaller Ktrans/larger τi. We find very similar behavior with a different therapy (phosphatase 2A re-activation) on a spontaneous murine breast tumor 39. Perhaps this pathway is common for therapy-induced tumor regression. The most parsimonious explanation is that a Ktrans decrease echoes a nutrient delivery decrease and then, subsequently, there is a decrease in metabolic activity signaled as a τi increase.

The correlation of the results we see at TP1 with the pathology results after 15 additional weeks of therapy (Fig. 3) is very encouraging. This is crucial for early, personalized therapy evaluation and adjustment. The two cases reported here exemplify this. If we had sufficient statistical experience that our approach informed clinical decisions, the therapy of the non-pCR patient might have been altered after TP1, and the therapy of the pCR patient might have been ended after TP1, or not switched after TP3.

The region of positive τi, Ktrans correlation in the rat gliosarcoma rim 32,55 coincides with the region of the implanted rat glioma that stains positive with EF5 55,80, a marker for hypoxia. This correlation is also positive for the RIF-1 tumor 33, which is known to be highly hypoxic 81. New results in a rat model of head and neck cancer show extensive overlap of an elevated τi region with that of EF5 staining 55. Also, increased tumor τi strongly correlates with survival times of human head and neck cancer patients (H. Poptani, personal communication). When τi is relatively large, the NKA activity is relatively small. Thus, it makes sense that Ktrans and τi are large and positively correlated in tissues where the cells may have entered a hypoxic state. Though the delivery of glucose is sufficient, it is not metabolized efficiently w.r.t. ATP synthesis 81,82.

The Ktrans value can be sensitive to the degree of tissue vascularization. If vascularization is low, the apparent Ktrans value decreases because, after extravasation, CA arrival in the tissue also requires diffusion 83. We do observe very small Ktrans and relatively large τi in breast adipose tissue 34,35. Presumably, this is due to the low vascularization. Also, in necrotic areas, one would expect Ktrans to be relatively small and τi to be relatively large, since cell metabolism should be slow.

Certainly, the spatial resolution of 1H2O MRI does not compare with that of the optical microscopy of pathology. A typical high-resolution MRI pixel covers 4 × 106 high power ‘20 × ‘ pixels ((0.5 µm)2) from a modern digital pathology microscope 84. However, the results presented here introduce the potentially highest resolution in vivo metabolic imaging.