Measurement of cellular-interstitial water exchange time in tumors based on diffusion-time-dependent diffusional kurtosis imaging

Diffusional kurtosis time dependence and the water exchange rate for the multi-compartment Kärger model

PURPOSE

To demonstrate an analytic formula giving the time dependence of the diffusional kurtosis for the Kärger model (KM) with an arbitrary number of exchanging compartments and its application in estimating the mean KM water exchange rate.

THEORY AND METHODS

The general formula for the kurtosis is derived from a power series solution for the multi-compartment KM. A lower bound on the exchange rate is established from the observation that the kurtosis is always a logarithmically convex function of time. Both the kurtosis time dependence and the lower bound are illustrated with numerical calculations. The lower bound is also applied to previously published data for the time dependence of the kurtosis in both brain and tumors.

RESULTS

The kurtosis for the multi-compartment KM is given by a sum in which each term is associated with an eigenvector of the exchange rate matrix. The lower bound is determined from the most negative value for the logarithmic derivative of the kurtosis with respect to time. In the cerebral cortex, the lower bound is found to vary from 15 to 76 s-1 , depending on the experimental details, while for the tumors considered, it varies from 2 to 4 s-1 .

CONCLUSION

The time dependence of the kurtosis for the multi-compartment KM has a simple analytic solution that allows a lower bound for the mean KM water exchange rate to be determined directly from experiment. This may be useful in tissues with complex microstructure that is difficult to model explicitly.

A Magnetic Resonance Imaging-Chemical Exchange Saturation Transfer (MRI-CEST) Method for the Detection of Water Cycling across Cellular Membranes

Water cycling across the membrane transporters is considered a hallmark of cellular metabolism and it could be of high diagnostic relevance in the characterization of tumors and other diseases. The method relies on the response of intracellular proton exchanging molecules to the presence of extracellular Gd-based contrast agents (GBCAs). Paramagnetic GBCAs enhances the relaxation rate of water molecules in the extracellular compartment and, through membrane exchange, the relaxation enhancement is transferred to intracellular molecules. The effect is detected at the MRI-CEST (Magnetic Resonance Imaging - Chemical Exchange Saturation Transfer) signal of intracellular proton exchanging molecules. The magnitude of the change in the CEST response reports on water cycling across the membrane. The method has been tested on Red Blood Cells and on orthotopic murine models of breast cancer with different degree of malignancy (4T1, TS/A and 168FARN). The distribution of voxels reporting on membrane permeability fits well with the cells' aggressiveness and acts as an early reporter to monitor therapeutic treatments.

Diffusion MRI with free gradient waveforms on a high-performance gradient system: Probing restriction and exchange in the human brain

The dependence of the diffusion MRI signal on the diffusion time carries signatures of restricted diffusion and exchange. Here we seek to highlight these signatures in the human brain by performing experiments using free gradient waveforms designed to be selectively sensitive to the two effects. We examine six healthy volunteers using both strong and ultra-strong gradients (80, 200 and 300 mT/m). In an experiment featuring a large set of 150 gradient waveforms with different sensitivities to restricted diffusion and exchange, our results reveal unique and different time-dependence signatures in grey and white matter. Grey matter was characterised by both restricted diffusion and exchange and white matter predominantly by restricted diffusion. Exchange in grey matter was at least twice as fast as in white matter, across all subjects and all gradient strengths. The cerebellar cortex featured relatively short exchange times (115 ms). Furthermore, we show that gradient waveforms with tailored designs can be used to map exchange in the human brain. We also assessed the feasibility of clinical applications of the method used in this work and found that the exchange-related contrast obtained with a 25-minute protocol at 300 mT/m was preserved in a 4-minute protocol at 300 mT/m and a 10-minute protocol at 80 mT/m. Our work underlines the utility of free waveforms for detecting time dependence signatures due to restricted diffusion and exchange in vivo, which may potentially serve as a tool for studying diseased tissue.

Probing brain tissue microstructure with MRI: principles, challenges, and the role of multidimensional diffusion-relaxation encoding

Diffusion MRI uses the random displacement of water molecules to sensitize the signal to brain microstructure and to properties such as the density and shape of cells. Microstructure modeling techniques aim to estimate these properties from acquired data by separating the signal between virtual tissue 'compartments' such as the intra-neurite and the extra-cellular space. A key challenge is that the diffusion MRI signal is relatively featureless compared with the complexity of brain tissue. Another challenge is that the tissue microstructure is wildly different within the gray and white matter of the brain. In this review, we use results from multidimensional diffusion encoding techniques to discuss these challenges and their tentative solutions. Multidimensional encoding increases the information content of the data by varying not only the b-value and the encoding direction but also additional experimental parameters such as the shape of the b-tensor and the echo time. Three main insights have emerged from such encoding. First, multidimensional data contradict common model assumptions on diffusion and T2 relaxation, and illustrates how the use of these assumptions cause erroneous interpretations in both healthy brain and pathology. Second, many model assumptions can be dispensed with if data are acquired with multidimensional encoding. The necessary data can be easily acquired in vivo using protocols optimized to minimize Cramér-Rao lower bounds. Third, microscopic diffusion anisotropy reflects the presence of axons but not dendrites. This insight stands in contrast to current 'neurite models' of brain tissue, which assume that axons in white matter and dendrites in gray matter feature highly similar diffusion. Nevertheless, as an axon-based contrast, microscopic anisotropy can differentiate gray and white matter when myelin alterations confound conventional MRI contrasts.

Frequency-dependent diffusion kurtosis imaging in the human brain using an oscillating gradient spin echo sequence and a high-performance head-only gradient

Measuring the time/frequency dependence of diffusion MRI is a promising approach to distinguish between the effects of different tissue microenvironments, such as membrane restriction, tissue heterogeneity, and compartmental water exchange. In this study, we measure the frequency dependence of diffusivity (D) and kurtosis (K) with oscillating gradient diffusion encoding waveforms and a diffusion kurtosis imaging (DKI) model in human brains using a high-performance, head-only MAGNUS gradient system, with a combination of b-values, oscillating frequencies (f), and echo time that has not been achieved in human studies before. Frequency dependence of diffusivity and kurtosis are observed in both global and local white matter (WM) and gray matter (GM) regions and characterized with a power-law model ∼Λ*fθ. The frequency dependences of diffusivity and kurtosis (including changes between fmin and fmax, Λ, and θ) vary over different WM and GM regions, indicating potential microstructural differences between regions. A trend of decreasing kurtosis over frequency in the short-time limit is successfully captured for in vivo human brains. The effects of gradient nonlinearity (GNL) on frequency-dependent diffusivity and kurtosis measurements are investigated and corrected. Our results show that the GNL has prominent scaling effects on the measured diffusivity values (3.5∼5.5% difference in the global WM and 6∼8% difference in the global cortex) and subsequently affects the corresponding power-law parameters (Λ, θ) while having a marginal influence on the measured kurtosis values (<0.05% difference) and power-law parameters (Λ, θ). This study expands previous OGSE studies and further demonstrates the translatability of frequency-dependent diffusivity and kurtosis measurements to human brains, which may provide new opportunities to probe human brain microstructure in health and disease.

Simultaneous estimation of the cellular water exchange rate, intracellular volume fraction, and longitudinal relaxation rate in cancer cells

The purpose of the current study was to investigate the feasibility of simultaneously estimating the cellular water efflux rate ( k ie ), intracellular longitudinal relaxation rate ( R 10 i ), and intracellular volume fraction ( v i ) of a cell suspension using multiple samples with different gadolinium concentrations. Numerical simulation studies were conducted to assess the uncertainty in the estimation of k ie , R 10 i , and v i from saturation recovery data using single (SC) or multiple concentrations (MC) of gadolinium-based contrast agent (GBCA). In vitro experiments with 4 T1 murine breast cancer and SCCVII squamous cell cancer models were conducted at 11 T to compare parameter estimation using the SC protocol with that using the MC protocol. The cell lines were challenged with a Na+ /K+ -ATPase inhibitor, digoxin, to assess the treatment response in terms of k ie , R 10 i , and v i . Data analysis was conducted using the two-compartment exchange model for parameter estimation. The simulation study data demonstrate that the MC method, compared with the SC method, reduces the uncertainty of the estimated k ie by decreasing the interquartile ranges from 27.3% ± 3.7% to 18.8% ± 5.1% and the median differences from ground truth from 15.0% ± 6.3% to 7.2% ± 4.2%, while estimating R 10 i and v i simultaneously. In the cell studies, the MC method demonstrated reduced uncertainty in overall parameter estimation compared with the SC approach. MC method-measured parameter changes in cells treated with digoxin increased R 10 i by 11.7% (p = 0.218) and k ie by 5.9% (p = 0.234) for 4 T1 cells, respectively, and decreased R 10 i by 28.8% (p = 0.226) and k ie by 1.6% (p = 0.751) for SCCVII cells, respectively. v i did not change noticeably by the treatment. The results of this study substantiate the feasibility of using saturation recovery data of multiple samples with different GBCA concentrations for simultaneous measurement of the cellular water efflux rate, intracellular volume fraction, and intracellular longitudinal relaxation rate in cancer cells.

Comprehensive Brain Tumour Characterisation with VERDICT-MRI: Evaluation of Cellular and Vascular Measures Validated by Histology

The aim of this work was to extend the VERDICT-MRI framework for modelling brain tumours, enabling comprehensive characterisation of both intra- and peritumoural areas with a particular focus on cellular and vascular features. Diffusion MRI data were acquired with multiple b-values (ranging from 50 to 3500 s/mm2), diffusion times, and echo times in 21 patients with brain tumours of different types and with a wide range of cellular and vascular features. We fitted a selection of diffusion models that resulted from the combination of different types of intracellular, extracellular, and vascular compartments to the signal. We compared the models using criteria for parsimony while aiming at good characterisation of all of the key histological brain tumour components. Finally, we evaluated the parameters of the best-performing model in the differentiation of tumour histotypes, using ADC (Apparent Diffusion Coefficient) as a clinical standard reference, and compared them to histopathology and relevant perfusion MRI metrics. The best-performing model for VERDICT in brain tumours was a three-compartment model accounting for anisotropically hindered and isotropically restricted diffusion and isotropic pseudo-diffusion. VERDICT metrics were compatible with the histological appearance of low-grade gliomas and metastases and reflected differences found by histopathology between multiple biopsy samples within tumours. The comparison between histotypes showed that both the intracellular and vascular fractions tended to be higher in tumours with high cellularity (glioblastoma and metastasis), and quantitative analysis showed a trend toward higher values of the intracellular fraction (fic) within the tumour core with increasing glioma grade. We also observed a trend towards a higher free water fraction in vasogenic oedemas around metastases compared to infiltrative oedemas around glioblastomas and WHO 3 gliomas as well as the periphery of low-grade gliomas. In conclusion, we developed and evaluated a multi-compartment diffusion MRI model for brain tumours based on the VERDICT framework, which showed agreement between non-invasive microstructural estimates and histology and encouraging trends for the differentiation of tumour types and sub-regions.

Evaluation of cellular water exchange in a mouse glioma model using dynamic contrast-enhanced MRI with two flip angles

This manuscript aims to evaluate the robustness and significance of the water efflux rate constant (k_io) parameter estimated using the two flip-angle Dynamic Contrast-Enhanced (DCE) MRI approach with a murine glioblastoma model at 7 T. The repeatability of contrast kinetic parameters and k_io measurement was assessed by a test-retest experiment (n = 7). The association of k_io with cellular metabolism was investigated through DCE-MRI and FDG-PET experiments (n = 7). Tumor response to a combination therapy of bevacizumab and fluorouracil (5FU) monitored by contrast kinetic parameters and k_io (n = 10). Test-retest experiments demonstrated compartmental volume fractions (v_e and v_p) remained consistent between scans while the vascular functional measures (F_p and PS) and k_io showed noticeable changes, most likely due to physiological changes of the tumor. The standardized uptake value (SUV) of tumors has a linear correlation with k_io (R² = 0.547), a positive correlation with F_p (R² = 0.504), and weak correlations with v_e (R² = 0.150), v_p (R² = 0.077), PS (R² = 0.117), K^trans (R² = 0.088) and whole tumor volume (R² = 0.174). In the treatment study, the k_io of the treated group was significantly lower than the control group one day after bevacizumab treatment and decreased significantly after 5FU treatment compared to the baseline. This study results support the feasibility of measuring k_io using the two flip-angle DCE-MRI approach in cancer imaging.

Time-dependent diffusivity and kurtosis in phantoms and patients with head and neck cancer

PURPOSE

To assess the reliability of measuring diffusivity, diffusional kurtosis, and cellular-interstitial water exchange time with long diffusion times (100-800 ms) using stimulated-echo DWI.

METHODS

Time-dependent diffusion MRI was tested on two well-established diffusion phantoms and in 5 patients with head and neck cancer. Measurements were conducted using an in-house diffusion-weighted STEAM-EPI pulse sequence with multiple diffusion times at a fixed TE on three scanners. We used the weighted linear least-squares fit method to estimate time-dependent diffusivity,D ( t ) $$ D(t) $$ , and diffusional kurtosis,K ( t ) $$ K(t) $$ . Additionally, the Kärger model was used to estimate cellular-interstitial water exchange time (τ ex $$ {\tau}_{ex} $$ ) fromK ( t ) $$ K(t) $$ .

RESULTS

Diffusivity measured by time-dependent STEAM-EPI measurements and commercial SE-EPI showed comparable results with R2 above 0.98 and overall 5.4 ± 3.0% deviation across diffusion times. Diffusional kurtosis phantom data showed expected patterns: constantD $$ D $$ andK $$ K $$  = 0 for negative controls and slow varyingD $$ D $$ andK $$ K $$ for samples made of nanoscopic vesicles. Time-dependent diffusion MRI in patients with head and neck cancer found that the Kärger model could be considered valid in 72% ± 23% of the voxels in the metastatic lymph nodes. The median cellular-interstitial water exchange time estimated for lesions was between 58.5 ms and 70.6 ms.

CONCLUSIONS

Based on two well-established diffusion phantoms, we found that time-dependent diffusion MRI measurements can provide stable diffusion and kurtosis values over a wide range of diffusion times and across multiple MRI systems. Moreover, estimation of cellular-interstitial water exchange time can be achieved using the Kärger model for the metastatic lymph nodes in patients with head and neck cancer.

Improving MR cell size imaging by inclusion of transcytolemmal water exchange

The goal of the current study is to include transcytolemmal water exchange in MR cell size imaging using the IMPULSED model for more accurate characterization of tissue cellular properties (e.g., apparent volume fraction of intracellular space v in ) and quantification of indicators of transcytolemmal water exchange. We propose a heuristic model that incorporates transcytolemmal water exchange into a multicompartment diffusion-based method (IMPULSED) that was developed previously to extract microstructural parameters (e.g., mean cell size d and apparent volume fraction of intracellular space v in ) assuming no water exchange. For t diff ≤ 5 ms, the water exchange can be ignored, and the signal model is the same as the IMPULSED model. For t diff ≥ 30 ms, we incorporated the modified Kärger model that includes both restricted diffusion and exchange between compartments. Using simulations and previously published in vitro cell data, we evaluated the accuracy and precision of model-derived parameters and determined how they are dependent on SNR and imaging parameters. The joint model provides more accurate d values for cell sizes ranging from 10 to 12 microns when water exchange is fast (e.g., intracellular water pre-exchange lifetime τ in ≤ 100 ms) than IMPULSED, and reduces the bias of IMPULSED-derived estimates of v in , especially when water exchange is relatively slow (e.g., τ in &gt; 200 ms). Indicators of transcytolemmal water exchange derived from the proposed joint model are linearly correlated with ground truth τ in values and can detect changes in cell membrane permeability induced by saponin treatment in murine erythroleukemia cancer cells. Our results suggest this joint model not only improves the accuracy of IMPULSED-derived microstructural parameters, but also provides indicators of water exchange that are usually ignored in diffusion models of tissues.

Preliminary study on intravoxel incoherent motion imaging and diffusion kurtosis imaging based on magnetic resonance imaging of normal kidneys in children

BACKGROUND

Renal disease in children may lead to a continuous decline of renal function. Multimodal functional magnetic resonance imaging (fMRI) technology can provide quantitative evaluation of renal function information. We investigated the feasibility of intravoxel incoherent motion imaging (IVIM) and diffusion kurtosis imaging (DKI) based on 3.0T MRI for the assessment of normal renal function in children and then analyzed the changes in functional parameters during development.

METHODS

A total of 132 children with normal function of both kidneys were grouped according to age: ≤1 year old, 1-≤2 years old, 2-≤3 years old, 3-≤10 years old, and 10-≤14 years old. All subjects received renal IVIM examinations to obtain the measured values of true diffusion coefficient (D), pseudo diffusion coefficient (Dp), perfusion fraction (f), and DKI examinations to obtain the mean diffusivity (MD) and mean kurtosis (MK) parameters of both kidneys. The differences of IVIM and DKI function indexes between the upper, middle and lower poles of the normal ipsilateral kidney, between the left and right kidneys, and between the renal cortex and medulla were compared. The correlations between the above parameters and age were analyzed.

RESULTS

There was no significant difference in the IVIM and DKI parameters between the upper, middle and lower poles in the ipsilateral kidney. There was no significant difference between bilateral kidneys. The D, MD, and MK values of the renal cortex and medulla at the same age were statistically different. The D and MD values of the renal cortex were higher than those of the medulla; the MK value of the renal medulla was higher than that of the cortex. The Dp and f values of the renal cortex and medulla were not statistically different. Except for Dp, all functional parameters of the remaining renal cortex and medulla were related to age.

CONCLUSIONS

IVIM and DKI functional imaging of children's normal kidneys can reflect the physiological characteristics and differences in the renal cortex and medulla, and their functional parameters have particular regularity with growth and development, suggesting that this technique has potential application value in children's kidney diseases.

Role of Transmembrane Water Exchange in Glioma Invasion/Migration: In Vivo Preclinical Study by Relaxometry at Very Low Magnetic Field

This work shows that the longitudinal relaxation differences observed at very low magnetic fields between invasion/migration and proliferation processes on glioma mouse models in vivo are related to differences in the transmembrane water exchange basically linked to the aquaporin expression changes. Three glioma mouse models were used: Glio6 and Glio96 as invasion/migration models and U87 as cell proliferation model. In vivo proton longitudinal relaxation-rate constants (R1) at very low fields were measured by fast field cycling NMR (FFC-NMR). The tumor contribution to the observed proton relaxation rate, R1tum (U87: 12.26 ± 0.64 s−1; Glio6: 3.76 ± 0.88 s−1; Glio96: 6.90 ± 0.64 s−1 at 0.01 MHz), and the intracellular water lifetime, τin (U87: 826 ± 19 ms; Glio6: 516 ± 8 ms; Glio96: 596 ± 15 ms), were found to be good diagnostic hallmarks to distinguish invasion/migration from proliferation (p < 0.01 and 0.001). Overexpression of AQP4 and AQP1 were assessed in invasion/migration models, highlighting the pathophysiological role of these two aquaporins in water exchange that, in turn, determine the lower values in the observed R1 relaxation rate constant in glioma invasion/migration. Overall, our findings demonstrate that τin and R1 (measured at very low fields) are relevant biomarkers, discriminating invasion/migration from proliferation in vivo. These results highlight the use of FFC-NMR and FFC-imaging to assess the efficiency of drugs that could modulate aquaporin functions.