Assessment of the effects of cellular tissue properties on ADC measurements by numerical simulation of water diffusion

Tutorial: a guide to diffusion MRI and structural connectomics

Diffusion magnetic resonance imaging (dMRI) is a versatile imaging technique that has gained popularity thanks to its sensitive ability to measure displacement of water molecules within a living tissue on a micrometer scale. Although dMRI has been around since the early 1990s, its applications are constantly evolving, primarily regarding the inference of structural connectomics from nerve fiber trajectories. However, these applications require expertise in image processing and statistics, and it can be difficult for a newcomer to choose an appropriate pipeline to fit their research needs, not least because dMRI is such a flexible methodology that dozens of acquisition and analysis pipelines have been developed over the years. This introductory guide is designed for graduate students and researchers in the neuroscience community who are interested in integrating this new methodology regardless of their background in neuroimaging and computational tools. The guide provides a brief overview of the basic dMRI methodologies but focuses on its applications in neuroplasticity and connectomics. The guide starts with dMRI experimental designs and a complete step-by-step pipeline for structural connectomics. The following section covers the basics of dMRI, including parameters and clinical applications (apparent diffusion coefficient, mean diffusivity, fractional anisotropy and microscopic fractional anisotropy), as well as different approaches and models. The final section focuses on structural connectomics, covering subjects from fiber tracking (techniques, evaluation and limitations) to structural networks (constructing, analyzing and visualizing a network).

Emergence of the brain-border immune niches and their contribution to the development of neurodegenerative diseases

Historically, the central nervous system (CNS) was regarded as 'immune-privileged', possessing its own distinct immune cell population. This immune privilege was thought to be established by a tight blood-brain barrier (BBB) and blood-cerebrospinal-fluid barrier (BCSFB), which prevented the crossing of peripheral immune cells and their secreted factors into the CNS parenchyma. However, recent studies have revealed the presence of peripheral immune cells in proximity to various brain-border niches such as the choroid plexus, cranial bone marrow (CBM), meninges, and perivascular spaces. Furthermore, emerging evidence suggests that peripheral immune cells may be able to infiltrate the brain through these sites and play significant roles in driving neuronal cell death and pathology progression in neurodegenerative disease. Thus, in this review, we explore how the brain-border immune niches may contribute to the pathogenesis of neurodegenerative disorders such as Alzheimer's disease (AD), Parkinson's disease (PD), and multiple sclerosis (MS). We then discuss several emerging options for harnessing the neuroimmune potential of these niches to improve the prognosis and treatment of these debilitative disorders using novel insights from recent studies.

Molecular Imaging with Aquaporin-Based Reporter Genes: Quantitative Considerations from Monte Carlo Diffusion Simulations

Aquaporins provide a unique approach for imaging genetic activity in deep tissues by increasing the rate of cellular water diffusion, which generates a magnetic resonance contrast. However, distinguishing aquaporin signals from the tissue background is challenging because water diffusion is influenced by structural factors, such as cell size and packing density. Here, we developed a Monte Carlo model to analyze how cell radius and intracellular volume fraction quantitatively affect aquaporin signals. We demonstrated that a differential imaging approach based on subtracting signals at two diffusion times can improve specificity by unambiguously isolating aquaporin signals from the tissue background. We further used Monte Carlo simulations to analyze the connection between diffusivity and the percentage of cells engineered to express aquaporin and established a mapping that accurately determined the volume fraction of aquaporin-expressing cells in mixed populations. The quantitative framework developed in this study will enable a broad range of applications in biomedical synthetic biology, requiring the use of aquaporins to noninvasively monitor the location and function of genetically engineered devices in live animals.

Extra-axonal contribution to double diffusion encoding-based pore size estimates in the corticospinal tract

OBJECTIVE

To study the origin of compartment size overestimation in double diffusion encoding MRI (DDE) in vivo experiments in the human corticospinal tract. Here, the extracellular space is hypothesized to be the origin of the DDE signal. By exploiting the DDE sensitivity to pore shape, it could be possible to identify the origin of the measured signal. The signal difference between parallel and perpendicular diffusion gradient orientation can indicate if a compartment is regular or eccentric in shape. As extracellular space can be considered an eccentric compartment, a positive difference would mean a high contribution to the compartment size estimates.

MATERIALS AND METHODS

Computer simulations using MISST and in vivo experiments in eight healthy volunteers were performed. DDE experiments using a double spin-echo preparation with eight perpendicular directions were measured in vivo. The difference between parallel and perpendicular gradient orientations was analyzed using a Wilcoxon signed-rank test and a Mann-Whitney U test.

RESULTS

Simulations and MR experiments showed a statistically significant difference between parallel and perpendicular diffusion gradient orientation signals ([Formula: see text]).

CONCLUSION

The results suggest that the DDE-based size estimate may be considerably influenced by the extra-axonal compartment. However, the experimental results are also consistent with purely intra-axonal contributions in combination with a large fiber orientation dispersion.

Molecular imaging with aquaporin-based reporter genes: quantitative considerations from Monte Carlo diffusion simulations

Aquaporins provide a new class of genetic tools for imaging molecular activity in deep tissues by increasing the rate of cellular water diffusion, which generates magnetic resonance contrast. However, distinguishing aquaporin contrast from the tissue background is challenging because water diffusion is also influenced by structural factors such as cell size and packing density. Here, we developed and experimentally validated a Monte Carlo model to analyze how cell radius and intracellular volume fraction quantitatively affect aquaporin signals. We demonstrated that a differential imaging approach based on time-dependent changes in diffusivity can improve specificity by unambiguously isolating aquaporin-driven contrast from the tissue background. Finally, we used Monte Carlo simulations to analyze the connection between diffusivity and the percentage of cells engineered to express aquaporin, and established a simple mapping that accurately determined the volume fraction of aquaporin-expressing cells in mixed populations. This study creates a framework for broad applications of aquaporins, particularly in biomedicine and in vivo synthetic biology, where quantitative methods to measure the location and performance of genetic devices in whole vertebrates are necessary.

Measurement of extracellular volume fraction using magnetic resonance-based conductivity tensor imaging

Conductivity tensor imaging (CTI) using MRI is an advanced method that can non-invasively measure the electrical properties of living tissues. The contrast of CTI is based on underlying hypothesis about the proportionality between the mobility and diffusivity of ions and water molecules inside tissues. The experimental validation of CTI in both in vitro and in vivo settings is required as a reliable tool to assess tissue conditions. The changes in extracellular space can be indicators for disease progression, such as fibrosis, edema, and cell swelling. In this study, we conducted a phantom imaging experiment to test the feasibility of CTI for measuring the extracellular volume fraction in biological tissue. To mimic tissue conditions with different extracellular volume fractions, four chambers of giant vesicle suspension (GVS) with different vesicle densities were included in the phantom. The reconstructed CTI images of the phantom were compared with the separately-measured conductivity spectra of the four chambers using an impedance analyzer. Moreover, the values of the estimated extracellular volume fraction in each chamber were compared with those measured by a spectrophotometer. As the vesicle density increased, we found that the extracellular volume fraction, extracellular diffusion coefficient, and low-frequency conductivity decreased, while the intracellular diffusion coefficient slightly increased. On the other hand, the high-frequency conductivity could not clearly distinguish the four chambers. The extracellular volume fraction measured by the spectrophotometer and CTI method in each chamber were quite comparable, i.e., (1.00, 0.98 ± 0.01), (0.59, 0.63 ± 0.02), (0.40, 0.40 ± 0.05), and (0.16, 0.18 ± 0.02). The prominent factor influencing the low-frequency conductivity at different GVS densities was the extracellular volume fraction. Further studies are needed to validate the CTI method as a tool to measure the extracellular volume fractions in living tissues with different intracellular and extracellular compartments.

Measurement of extracellular volume fraction using magnetic resonance-based conductivity tensor imaging

Conductivity tensor imaging (CTI) using MRI is an advanced method that can non-invasively measure the electrical properties of living tissues. The contrast of CTI is based on underlying hypothesis about the proportionality between the mobility and diffusivity of ions and water molecules inside tissues. The experimental validation of CTI in both in vitro and in vivo settings is required as a reliable tool to assess tissue conditions. The changes in extracellular space can be indicators for disease progression, such as fibrosis, edema, and cell swelling. In this study, we conducted a phantom imaging experiment to test the feasibility of CTI for measuring the extracellular volume fraction in biological tissue. To mimic tissue conditions with different extracellular volume fractions, four chambers of giant vesicle suspension (GVS) with different vesicle densities were included in the phantom. The reconstructed CTI images of the phantom were compared with the separately-measured conductivity spectra of the four chambers using an impedance analyzer. Moreover, the values of the estimated extracellular volume fraction in each chamber were compared with those measured by a spectrophotometer. As the vesicle density increased, we found that the extracellular volume fraction, extracellular diffusion coefficient, and low-frequency conductivity decreased, while the intracellular diffusion coefficient slightly increased. On the other hand, the high-frequency conductivity could not clearly distinguish the four chambers. The extracellular volume fraction measured by the spectrophotometer and CTI method in each chamber were quite comparable, i.e., (1.00, 0.98 ± 0.01), (0.59, 0.63 ± 0.02), (0.40, 0.40 ± 0.05), and (0.16, 0.18 ± 0.02). The prominent factor influencing the low-frequency conductivity at different GVS densities was the extracellular volume fraction. Further studies are needed to validate the CTI method as a tool to measure the extracellular volume fractions in living tissues with different intracellular and extracellular compartments.

Diffusion MRI with pulsed and free gradient waveforms: Effects of restricted diffusion and exchange

Monitoring time dependence with diffusion MRI yields observables sensitive to compartment sizes (restricted diffusion) and membrane permeability (water exchange). However, restricted diffusion and exchange have opposite effects on the diffusion-weighted signal, which can lead to errors in parameter estimates. In this work, we propose a signal representation that incorporates the effects of both restricted diffusion and exchange up to second order in b-value and is compatible with gradient waveforms of arbitrary shape. The representation features mappings from a gradient waveform to two scalars that separately control the sensitivity to restriction and exchange. We demonstrate that these scalars span a two-dimensional space that can be used to choose waveforms that selectively probe restricted diffusion or exchange, eliminating the correlation between the two phenomena. We found that waveforms with specific but unconventional shapes provide an advantage over conventional pulsed and oscillating gradient acquisitions. We also show that parametrization of waveforms into a two-dimensional space can be used to understand protocols from other approaches that probe restricted diffusion and exchange. For example, we found that the variation of mixing time in filter-exchange imaging corresponds to variation of our exchange-weighting scalar at a fixed value of the restriction-weighting scalar. The proposed signal representation was evaluated using Monte Carlo simulations in identical parallel cylinders with hexagonal and random packing as well as parallel cylinders with gamma-distributed radii. Results showed that the approach is sensitive to sizes in the interval 4-12 μm and exchange rates in the simulated range of 0 to 20 s - 1 , but also that there is a sensitivity to the extracellular geometry. The presented theory constitutes a simple and intuitive description of how restricted diffusion and exchange influence the signal as well as a guide to protocol design capable of separating the two effects.

Apparent Diffusion Coefficient Can Predict Therapy Response of Hepatocellular Carcinoma to Transcatheter Arterial Chemoembolization

AIM

The goal of this meta-analysis was to assess the apparent diffusion coefficient (ADC) as a pre- and posttreatment (ADC value changes [ΔADC]) predictive imaging biomarker of response to transcatheter arterial chemoembolization (TACE) in patients with hepatocellular carcinoma (HCC).

METHODS

Scopus database, Embase database, and MEDLINE library were scanned for connections between pre- and posttreatment ADC values of HCC and response to TACE. Six studies qualified for inclusion. The following parameters were collected: authors, publication year, study design, number of patients, drugs for TACE, mean ADC value, standard deviation, measure method, b values, and Tesla strength. The Quality Assessment of Diagnostic Studies 2 instrument was employed to check the methodological quality of each study. The meta-analysis was performed by utilizing RevMan 5.3 software. DerSimonian and Laird random-effects models with inverse-variance were used to regard heterogeneity. The mean ADC values and 95% confidence intervals were computed.

RESULTS

Six studies (n = 271 patients with 293 HCC nodules) were included. The pretreatment mean ADC in the responder group was 1.20 × 10-3 mm2/s (0.98, 1.42) and 1.14 × 10-3 mm2/s (0.89, 1.39) in the nonresponder group. The analysis of post-TACE ΔADC revealed a threshold of ≥20% to identify treatment responders. No suitable pretreatment ADC threshold to predict therapy response or discriminate between responders and nonresponders before therapy could be discovered.

CONCLUSION

ΔADC can facilitate early objective response evaluation through post-therapeutic ADC alterations ≥20%. Pretreatment ADC cannot predict response to TACE.

Neurite Exchange Imaging (NEXI): A minimal model of diffusion in gray matter with inter-compartment water exchange

Biophysical models of diffusion in white matter have been center-stage over the past two decades and are essentially based on what is now commonly referred to as the "Standard Model" (SM) of non-exchanging anisotropic compartments with Gaussian diffusion. In this work, we focus on diffusion MRI in gray matter, which requires rethinking basic microstructure modeling blocks. In particular, at least three contributions beyond the SM need to be considered for gray matter: water exchange across the cell membrane - between neurites and the extracellular space; non-Gaussian diffusion along neuronal and glial processes - resulting from structural disorder; and signal contribution from soma. For the first contribution, we propose Neurite Exchange Imaging (NEXI) as an extension of the SM of diffusion, which builds on the anisotropic Kärger model of two exchanging compartments. Using datasets acquired at multiple diffusion weightings (b) and diffusion times (t) in the rat brain in vivo, we investigate the suitability of NEXI to describe the diffusion signal in the gray matter, compared to the other two possible contributions. Our results for the diffusion time window 20-45 ms show minimal diffusivity time-dependence and more pronounced kurtosis decay with time, which is well fit by the exchange model. Moreover, we observe lower signal for longer diffusion times at high b. In light of these observations, we identify exchange as the mechanism that best explains these signal signatures in both low-b and high-b regime, and thereby propose NEXI as the minimal model for gray matter microstructure mapping. We finally highlight multi-b multi-t acquisition protocols as being best suited to estimate NEXI model parameters reliably. Using this approach, we estimate the inter-compartment water exchange time to be 15 - 60 ms in the rat cortex and hippocampus in vivo, which is of the same order or shorter than the diffusion time in typical diffusion MRI acquisitions. This suggests water exchange as an essential component for interpreting diffusion MRI measurements in gray matter.

The Effect of Dehydroepiandrosterone Treatment on Neurogenesis, Astrogliosis and Long-Term Cocaine-Seeking Behavior in a Cocaine Self-Administration Model in Rats

Cocaine addiction is an acquired behavioral state developed in vulnerable individuals after cocaine exposure. It is characterized by compulsive drug-seeking and high vulnerability to relapse even after prolonged abstinence, associated with decreased neurogenesis in the hippocampus. This addictive state is hypothesized to be a form of “memory disease” in which the drug exploits the physiological neuroplasticity mechanisms that mediate regular learning and memory processes. Therefore, a major focus of the field has been to identify the cocaine-induced neuroadaptations occurring in the usurped brain’s reward circuit. The neurosteroid dehydroepiandrosterone (DHEA) affects brain cell morphology, differentiation, neurotransmission, and memory. It also reduces drug-seeking behavior in an animal model of cocaine self-administration. Here, we examined the long-lasting effects of DHEA treatment on the attenuation of cocaine-seeking behavior. We also examined its short- and long-term influence on hippocampal cells architecture (neurons and astrocytes). Using a behavioral examination, immunohistochemical staining, and diffusion tensor imaging, we found an immediate effect on tissue density and activation of astrocytes, which has a continuous beneficial effect on neurogenesis and tissue organization. This research emphasizes the requites concert between astrocytes and neurons in the rehabilitation from addiction behavior. Thus, DHEA may serve as a treatment that corrects brain damage following exposure to and abstinence from cocaine.

The relationship between diffusion heterogeneity and microstructural changes in high-grade gliomas using Monte Carlo simulations

PURPOSE

Diffusion-weighted imaging (DWI) may aid accurate tumor grading. Decreased diffusivity and increased diffusion heterogeneity measures have been observed in high-grade gliomas using the non-monoexponential models for DWI. However, DWI measures concerning tissue characteristics in terms of pathophysiological and structural changes are yet to be established. Thus, this study aims to investigate the relationship between the diffusion measurements and microstructural changes in the presence of high-grade gliomas using a three-dimensional Monte Carlo simulation with systematic changes of microstructural parameters.

METHODS

Water diffusion was simulated in a microenvironment along with changes associated with the presence of high-grade gliomas, including increases in cell density, nuclear volume, extracellular volume (VF_ex), and extracellular tortuosity (λ_ex), and changes in membrane permeability (P_mem). DWI signals were simulated using a pulsed gradient spin-echo sequence. The sequence parameters, including the maximum gradient strength and diffusion time, were set to be comparable to those of clinical scanners and advanced human MRI systems. The DWI signals were fitted using the gamma distribution and diffusional kurtosis models with b-values up to 6000 and 2500 s/mm², respectively.

RESULTS

The diffusivity measures (apparent diffusion coefficients (ADC), D_gamma of the gamma distribution model and D_app of the diffusional kurtosis model) decreased with increases in cell density and λ_ex, and a decrease in P_mem. These diffusivity measures increased with increases in nuclear volume and VF_ex. The diffusion heterogeneity measures (σ_gamma of the gamma distribution model and K_app of the diffusional kurtosis model) increased with increases in cell density or nuclear volume at the low P_mem, and a decrease in P_mem. Increased σ_gamma was also associated with an increase in VF_ex.

CONCLUSION

Among simulated microstructural changes, only increases in cell density at low P_mem or decreases in P_mem corresponded to both the decreased diffusivity and increased diffusion heterogeneity measures. The results suggest that increases in cell density at low P_mem or decreases in P_mem may be associated with the diffusion changes observed in high-grade gliomas.

Accuracy and precision of apparent diffusion coefficient measurements on a 1.5 T MR-Linac in central nervous system tumour patients

BACKGROUND AND PURPOSE

MRI linear accelerators (MR-Linacs) may allow treatment adaptation to be guided by quantitative MRI including diffusion-weighted imaging (DWI). The aim of this study was to evaluate the accuracy and precision of apparent diffusion coefficient (ADC) measurements from DWI on a 1.5 T MR-Linac in patients with central nervous system (CNS) tumours through comparison with a diagnostic scanner.

MATERIALS AND METHODS

CNS patients were treated using a 1.5 T Elekta Unity MR-Linac. DWI was acquired during MR-Linac treatment and on a Philips Ingenia 1.5 T. The agreement between the two scanners on median ADC over the gross tumour/clinical target volumes (GTV/CTV) and in brain regions (white/grey matter, cerebrospinal fluid (CSF)) was computed. Repeated scans were used to estimate ADC repeatability. Daily changes in ADC over the GTV of high-grade gliomas were characterized from MR-Linac scans.

RESULTS

DWI from 59 patients was analyzed. MR-Linac ADC measurements showed a small bias relative to Ingenia measurements in white matter, grey matter, GTV, and CTV (bias: -0.05 ± 0.03, -0.08 ± 0.05, -0.1 ± 0.1, -0.08 ± 0.07 μm²/ms). ADC differed substantially in CSF (bias: -0.5 ± 0.3 μm²/ms). The repeatability of MR-Linac ADC over white/grey matter was similar to previous reports (coefficients of variation for median ADC: 1.4%/1.8%). MR-Linac ADC changes in the GTV were detectable.

CONCLUSIONS

It is possible to obtain ADC measurements in the brain on a 1.5 T MR-Linac that are comparable to those of diagnostic-quality scanners. This technical validation study adds to the foundation for future studies that will correlate brain tumour ADC with clinical outcomes.

Reduced diffusion in white matter after radiotherapy with photons and protons

BACKGROUND AND PURPOSE

Radio(chemo)therapy is standard in the adjuvant treatment of glioblastoma. Inevitably, brain tissue surrounding the target volume is also irradiated, potentially causing acute and late side-effects. Diffusion imaging has been shown to be a sensitive method to detect early changes in the cerebral white matter (WM) after radiation. The aim of this work was to assess possible changes in the mean diffusivity (MD) of WM after radio(chemo)therapy using Diffusion-weighted imaging (DWI) and to compare these effects between patients treated with proton and photon irradiation.

MATERIALS AND METHODS

70 patients with glioblastoma underwent adjuvant radio(chemo)therapy with protons (n = 20) or photons (n = 50) at the University Hospital Dresden. MRI follow-ups were performed at three-monthly intervals and in this study were evaluated until 33 months after the end of therapy. Relative white matter MD changes between baseline and all follow-up visits were calculated in different dose regions.

RESULTS

We observed a significant decrease of MD (p < 0.05) in WM regions receiving more than 20 Gy. MD reduction was progressive with dose and time after radio(chemo)therapy (maximum: -7.9 ± 1.2% after 24 months, ≥50 Gy). In patients treated with photons, significant reductions of MD in the entire WM (p < 0.05) were seen at all time points. Conversely, in proton patients, whole brain MD did not change significantly.

CONCLUSIONS

Irradiation leads to measurable MD reduction in white matter, progressing with both increasing dose and time. Treatment with protons reduces this effect most likely due to a lower total dose in the surrounding white matter. Further investigations are needed to assess whether those MD changes correlate with known radiation induced side-effects.

Assessment of the effects of mimicking tissue microstructural properties on apparent diffusion coefficient and apparent exchange rate in diffusion MRI via a series of specially designed phantoms

PURPOSE

Diffusion MRI provides a valuable tool for imaging tissue microstructure. However, due to the lack of related experimental methods and specially designed phantoms, no experimental study has been conducted yet to quantitatively assess the effects of membrane permeability, intracellular volume fraction (IVF), and intracellular diffusivity on the apparent diffusion coefficient (ADC) obtained from diffusion weighted imaging (DWI), and the effects of membrane permeability on the apparent exchange rate (AXR) obtained from filter exchange imaging (FEXI).

METHODS

A series of phantoms with three adjustable parameters was designed to mimic tissue microstructural properties including membrane permeability, IVF, and intracellular diffusivity. Quantitative experiments were conducted to assess the effects of these properties on ADC and AXR. DWI scans were performed to obtain axial and radial ADC values. FEXI scans were performed to obtain AXR values.

RESULTS

Axial ADC values range from 1.148 μm² /ms to 2.157 μm² /ms, and radial ADC values range from 0.904 μm² /ms to 2.067 μm² /ms. Radial ADC decreased with a decrease in fiber permeability. Decreased axial and radial ADC values with increased intra-fiber volume fraction, and increased polyvinylpyrrolidone (PVP) concentration of the intra-fiber space were observed. AXR values range from 2.1 s^-1 to 4.9 s^-1 . AXR increases with fiber permeability.

CONCLUSION

The proposed phantoms can quantitatively evaluate the effects of mimicking tissue microstructural properties on ADC and AXR. This new phantom design provides a potential method for further understanding the biophysical mechanisms underlying the change in ADC and diffusion exchange.

Investigating the relationship between diffusion kurtosis tensor imaging (DKTI) and histology within the normal human brain

Measurements of water diffusion with MRI have been used as a biomarker of tissue microstructure and heterogeneity. In this study, diffusion kurtosis tensor imaging (DKTI) of the brain was undertaken in 10 healthy volunteers at a clinical field strength of 3 T. Diffusion and kurtosis metrics were measured in regions-of-interest on the resulting maps and compared with quantitative analysis of normal post-mortem tissue histology from separate age-matched donors. White matter regions showed low diffusion (0.60 ± 0.04 × 10-3 mm2/s) and high kurtosis (1.17 ± 0.06), consistent with a structured heterogeneous environment comprising parallel neuronal fibres. Grey matter showed intermediate diffusion (0.80 ± 0.02 × 10-3 mm2/s) and kurtosis (0.82 ± 0.05) values. An important finding is that the subcortical regions investigated (thalamus, caudate and putamen) showed similar diffusion and kurtosis properties to white matter. Histological staining of the subcortical nuclei demonstrated that the predominant grey matter was permeated by small white matter bundles, which could account for the similar kurtosis to white matter. Quantitative histological analysis demonstrated higher mean tissue kurtosis and vector standard deviation values for white matter (1.08 and 0.81) compared to the subcortical regions (0.34 and 0.59). Mean diffusion on DKTI was positively correlated with tissue kurtosis (r = 0.82, p < 0.05) and negatively correlated with vector standard deviation (r = -0.69, p < 0.05). This study demonstrates how DKTI can be used to study regional structural variations in the cerebral tissue microenvironment and could be used to probe microstructural changes within diseased tissue in the future.

Portable simulation framework for diffusion MRI

The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite element discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite element discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite element software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.

Apparent diffusion coefficient cannot predict molecular subtype and lymph node metastases in invasive breast cancer: a multicenter analysis

Background

Radiological imaging plays a central role in the diagnosis of breast cancer (BC). Some studies suggest MRI techniques like diffusion weighted imaging (DWI) may provide further prognostic value by discriminating between tumors with different biologic characteristics including receptor status and molecular subtype. However, there is much contradictory reported data regarding such associations in the literature. The purpose of the present study was to provide evident data regarding relationships between quantitative apparent diffusion coefficient (ADC) values on DWI and pathologic prognostic factors in BC.

Methods

Data from 5 centers (661 female patients, mean age, 51.4 ± 10.5 years) were acquired. Invasive ductal carcinoma (IDC) was diagnosed in 625 patients (94.6%) and invasive lobular carcinoma in 36 cases (5.4%). Luminal A carcinomas were diagnosed in 177 patients (28.0%), luminal B carcinomas in 279 patients (44.1%), HER 2+ carcinomas in 66 cases (10.4%), and triple negative carcinomas in 111 patients (17.5%). The identified lesions were staged as T1 in 51.3%, T2 in 43.0%, T3 in 4.2%, and as T4 in 1.5% of the cases. N0 was found in 61.3%, N1 in 33.1%, N2 in 2.9%, and N3 in 2.7%. ADC values between different groups were compared using the Mann–Whitney U test and by the Kruskal-Wallis H test. The association between ADC and Ki 67 values was calculated by Spearman’s rank correlation coefficient.

Results

ADC values of different tumor subtypes overlapped significantly. Luminal B carcinomas had statistically significant lower ADC values compared with luminal A (p = 0.003) and HER 2+ (p = 0.007) lesions. No significant differences of ADC values were observed between luminal A, HER 2+ and triple negative tumors. There were no statistically significant differences of ADC values between different T or N stages of the tumors. Weak statistically significant correlation between ADC and Ki 67 was observed in luminal B carcinoma (r = − 0.130, p = 0.03). In luminal A, HER 2+ and triple negative tumors there were no significant correlations between ADC and Ki 67.

Conclusion

ADC was not able to discriminate molecular subtypes of BC, and cannot be used as a surrogate marker for disease stage or proliferation activity.

Diffusion-weighted MRI and 18F-FDG PET correlation with immunity in early radiotherapy response in BNL hepatocellular carcinoma mouse model: timeline validation

PURPOSE

Imaging probes/biomarkers that are correlated with molecular or microenvironmental alterations in tumors have been used not only in diagnosing cancer but also in assessing the efficacy of cancer treatment. We evaluated the early response of hepatocellular carcinoma (HCC) to radiation treatment using T2-weighted magnetic resonance imaging (MRI), diffusion-weighted (DW) MRI, and ¹⁸F-fluorodeoxyglucose (¹⁸F-FDG) positron emission tomography (PET).

METHODS

Orthotopic HCC tumors were established in the right liver lobe of Balb/c mice. Mice were longitudinally scanned using T2-weighted/DW MRI and ¹⁸F-FDG PET 1 day before and on days 1, 3, 6, 9 and 13 after irradiation with 15 Gy to the right liver lobe to determine tumor size, apparent diffusion coefficient (ADC) value, and maximum standardized uptake value. Immunohistochemical (IHC) staining was performed to validate the tumor microenvironment.

RESULTS

Irradiation markedly retarded tumor growth in the orthotopic HCC model and led to increaes in ADC values as early as on day 1 after irradiation. Irradiation also resulted in increases in ¹⁸F-FDG uptake on day 1 that were sustained until the end of the observation period. IHC staining revealed a decrease in the number of proliferative cells and a continuous macrophage influx into irradiated tumors, which dramatically altered the tumor microenvironment. Lastly, in vitro coculture of HCC cells and macrophages led to interaction between the cells and enhanced the cellular uptake of ¹⁸F-FDG.

CONCLUSION

ADC values and ¹⁸F-FDG uptake measured using DW MRI and ¹⁸F-FDG PET serve as potential biomarkers for early assessment of HCC tumor responses to radiation therapy.

Prediction of survival with combining quantitative 18 F-FDG PET/CT and DW-MRI parameters in sinonasal malignancies

BACKGROUND

We aimed to establish the prognostic value of ¹⁸ F-fluoro-deoxy-glucose positron emission/CT (¹⁸ F-FDG PET/CT) and diffusion-weighted (DW) MRI in determining overall survival (OS), progression-free survival (PFS), and distant metastasis-free survival (DMFS) of sinonasal malignancies.

METHODS

Sixty-eight patients with sinonasal cancer who underwent both pretreatment ¹⁸ F-FDG PET/CT scan and head-neck MRI from January 2009 through August 2017 were retrospectively reviewed. Kaplan-Meier survival analysis of ¹⁸ F-FDG PET/CT and DW-MRI parameters were performed for OS, PFS, and DMFS.

RESULTS

Cox regression analysis determined that all the quantitative ¹⁸ F-FDG PET/CT and DW-MRI parameters were independently correlated with PFS, DMFS, and OS (P < .05). After controlling for imaging variables, perineural invasion (P = .02) and ill-defined margin (P = .02) were found to be significantly correlated with shorter OS; while the perineural invasion was significantly correlated with shorter PFS (P = .02).

CONCLUSIONS

The pretreatment DW-MRI and ¹⁸ F-FDG PET/CT parameters could be substantial surrogate markers for sinonasal malignancies.

Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds

The Bloch-Torrey partial differential equation can be used to describe the evolution of the transverse magnetization of the imaged sample under the influence of diffusion-encoding magnetic field gradients inside the MRI scanner. The integral of the magnetization inside a voxel gives the simulated diffusion MRI signal. This paper proposes a finite element discretization on manifolds in order to efficiently simulate the diffusion MRI signal in domains that have a thin layer or a thin tube geometrical structure. The variable thickness of the three-dimensional domains is included in the weak formulation established on the manifolds. We conducted a numerical study of the proposed approach by simulating the diffusion MRI signals from the extracellular space (a thin layer medium) and from neurons (a thin tube medium), comparing the results with the reference signals obtained using a standard three-dimensional finite element discretization. We show good agreements between the simulated signals using our proposed method and the reference signals for a wide range of diffusion MRI parameters. The approximation becomes better as the diffusion time increases. The method helps to significantly reduce the required simulation time, computational memory, and difficulties associated with mesh generation, thus opening the possibilities to simulating complicated structures at low cost for a better understanding of diffusion MRI in the brain.

Physical and numerical phantoms for the validation of brain microstructural MRI: A cookbook

Phantoms, both numerical (software) and physical (hardware), can serve as a gold standard for the validation of MRI methods probing the brain microstructure. This review aims to provide guidelines on how to build, implement, or choose the right phantom for a particular application, along with an overview of the current state-of-the-art of phantoms dedicated to study brain microstructure with MRI. For physical phantoms, we discuss the essential requirements and relevant characteristics of both the (NMR visible) liquid and (NMR invisible) phantom materials that induce relevant microstructural features detectable via MRI, based on diffusion, intra-voxel incoherent motion, magnetization transfer or magnetic susceptibility weighted contrast. In particular, for diffusion MRI, many useful phantoms have been proposed, ranging from simple liquids to advanced biomimetic phantoms consisting of hollow or plain microfibers and capillaries. For numerical phantoms, the focus is on Monte Carlo simulations of random walk, for which the basic principles, along with useful criteria to check and potential pitfalls are reviewed, in addition to a literature overview highlighting recent advances. While many phantoms exist already, the current review aims to stimulate further research in the field and to address remaining needs.

Quantifying myofiber integrity using diffusion MRI and random permeable barrier modeling in skeletal muscle growth and Duchenne muscular dystrophy model in mice

PURPOSE

To measure the microstructural changes during skeletal muscle growth and progressive pathologies using the random permeable model with diffusion MRI, and compare findings to conventional imaging modalities such as three-point Dixon and T2 imaging.

METHODS

In vivo and ex vivo DTI experiments with multiple diffusion times (20-700 ms) were completed on wild-type (n = 22) and muscle-dystrophic mdx mice (n = 8) at various developmental time points. The DTI data were analyzed with the random permeable model framework that provides estimates of the unrestricted diffusion coefficient (D0 ), membrane surface-to-volume ratio (S/V), and membrane permeability (κ). In addition, the MRI experiments included conventional measures, such as tissue fat fractions and T2 relaxation.

RESULTS

During normal muscle growth between week 4 and week 13, the in vivo S/V, fractional anisotropy, and fat fraction correlated positively with age (ρ = 0.638, 0.664, and 0.686, respectively), whereas T2 correlated negatively (ρ = -0.847). In mdx mice, all DTI random permeable model parameters and fat fraction had significant positive correlation with age, whereas fractional anisotropy and T2 did not have significant correlation with age. Histological measurements of the perimeter-to-area ratio served as a proxy for the model-derived S/V in the cylindrical myofiber geometry, and had a significant correlation with the ex vivo S/V (r = 0.71) as well as the in vivo S/V (r = 0.56).

CONCLUSION

The present study demonstrates that DTI at multiple diffusion times with the random permeable model analysis allows for noninvasively quantifying muscle fiber microstructural changes during both normal muscle growth and disease progression. Future studies can apply our technique to evaluate current and potential treatments to muscle myopathies.

A biomimetic tumor tissue phantom for validating diffusion-weighted MRI measurements

PURPOSE

To develop a biomimetic tumor tissue phantom which more closely reflects water diffusion in biological tissue than previously used phantoms, and to evaluate the stability of the phantom and its potential as a tool for validating diffusion-weighted (DW) MRI measurements.

METHODS

Coaxial-electrospraying was used to generate micron-sized hollow polymer spheres, which mimic cells. The bulk structure was immersed in water, providing a DW-MRI phantom whose apparent diffusion coefficient (ADC) and microstructural properties were evaluated over a period of 10 months. Independent characterization of the phantom's microstructure was performed using scanning electron microscopy (SEM). The repeatability of the construction process was investigated by generating a second phantom, which underwent high resolution synchrotron-CT as well as SEM and MR scans.

RESULTS

ADC values were stable (coefficients of variation (CoVs) < 5%), and varied with diffusion time, with average values of 1.44 ± 0.03 µm2 /ms (Δ = 12 ms) and 1.20 ± 0.05 µm2 /ms (Δ = 45 ms). Microstructural parameters showed greater variability (CoVs up to 13%), with evidence of bias in sphere size estimates. Similar trends were observed in the second phantom.

CONCLUSION

A novel biomimetic phantom has been developed and shown to be stable over 10 months. It is envisaged that such phantoms will be used for further investigation of microstructural models relevant to characterizing tumor tissue, and may also find application in evaluating acquisition protocols and comparing DW-MRI-derived biomarkers obtained from different scanners at different sites. Magn Reson Med 80:147-158, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Whole lesion histogram analysis of meningiomas derived from ADC values. Correlation with several cellularity parameters, proliferation index KI 67, nucleic content, and membrane permeability

PURPOSE

To analyze several histopathological features and their possible correlations with whole lesion histogram analysis derived from ADC maps in meningioma.

MATERIALS AND METHODS

The retrospective study involved 36 patients with primary meningiomas. For every tumor, the following histogram analysis parameters of apparent diffusion coefficient (ADC) were calculated: ADC_mean, ADC_max, ADC_min, ADC_median, ADC_mode, ADC percentiles: P10, P25, P75, P90, as well kurtosis, skewness, and entropy. All measures were performed by two radiologists. Proliferation index KI 67, minimal, maximal and mean cell count, total nucleic area, and expression of water channel aquaporin 4 (AQP4) were estimated. Spearman's correlation coefficient was used to analyze associations between investigated parameters.

RESULTS

A perfect interobserver agreement for all ADC values (0.84-0.97) was identified. All ADC values correlated inversely with tumor cellularity with the strongest correlation between P10, P25 and mean cell count (-0.558). KI 67 correlated inversely with all ADC values except ADC_min. ADC parameters did not correlate with total nucleic area. All ADC values correlated statistically significant with expression of AQP4.

CONCLUSIONS

ADC histogram analysis is a valid method with an excellent interobserver agreement. Cellularity parameters and proliferation potential are associated with different ADC values. Membrane permeability may play a greater role for water diffusion than cell count and proliferation activity.

Histogram analysis of ADC in rectal cancer: associations with different histopathological findings including expression of EGFR, Hif1-alpha, VEGF, p53, PD1, and KI 67. A preliminary study

Functional imaging modalities like Diffusion-weighted imaging are increasingly used to predict tumor behavior like cellularity and vascularity in different tumors. Histogram analysis is an emergent imaging analysis, in which every voxel is used to obtain a histogram and therefore statistically information about tumors can be provided. The purpose of this study was to elucidate possible associations between ADC histogram parameters and several immunhistochemical features in rectal cancer. Overall, 11 patients with histologically proven rectal cancer were included into the study. There were 2 (18.18%) females and 9 males with a mean age of 67.1 years. KI 67-index, expression of p53, EGFR, VEGF, and Hif1-alpha were semiautomatically estimated. The tumors were divided into PD1-positive and PD1-negative lesions. ADC histogram analysis was performed as a whole lesion measurement using an in-house matlab application. Spearman's correlation analysis revealed a strong correlation between EGFR expression and ADCmax (p=0.72, P=0.02). None of the vascular parameters (VEGF, Hif1-alpha) correlated with ADC parameters. Kurtosis and skewness correlated inversely with p53 expression (p=-0.64, P=0.03 and p=-0.81, P=0.002, respectively). ADCmedian and ADCmode correlated with Ki67 (p=-0.62, P=0.04 and p=-0.65, P=0.03, respectively). PD1-positive tumors showed statistically significant lower ADCmax values in comparison to PD1-negative tumors, 1.93 ± 0.36 vs 2.32 ± 0.47×10^-3mm²/s, p=0.04. Several associations were identified between histogram parameter derived from ADC maps and EGFR, KI 67 and p53 expression in rectal cancer. Furthermore, ADCmax was different between PD1 positive and PD1 negative tumors indicating an important role of ADC parameters for possible future treatment prediction.

Proving of a Mathematical Model of Cell Calculation Based on Apparent Diffusion Coefficient

OBJECTIVES: Recently, Atuegwu et al. proposed a mathematical model based on ADC_mean and ADC_min to calculation of cellularity. Our purpose was to compare the calculated cellularity according to the formula with the estimated cell count by histopathology in different tumors. METHODS: For this study, we re-analyzed our previous data regarding associations between ADC parameters and histopathological findings. Overall, 134 patients with different tumors were acquired for the analysis. For all tumors, the number of tumor cells was calculated according to Atuegwu et al. 2013. We performed a correlation analysis between the calculated and estimated cellularity. Thereby, Pearson's correlation coefficient was used and P < .05 was taken to indicate statistical significance in all instances. RESULTS: The estimated and calculated cellularity correlated well together in HNSCC (r = 0.701, P = .016) and lymphomas (r = 0.661, P = .001), and moderately in rectal cancer (r = 0.510, P = .036). There were no statistically significant correlations between the estimated and calculated cellularity in uterine cervical cancer, meningiomas, and in thyroid cancer. CONCLUSION: The proposed formula for cellularity calculation does not apply for all tumors. It may be used for HNSCC, cerebral lymphomas and rectal cancer, but not for uterine cervical cancer, meningioma, and thyroid cancer. Furthermore, its usefulness should be proved for other tumors.

Correlation between apparent diffusion coefficient (ADC) and cellularity is different in several tumors: a meta-analysis

The purpose of this meta-analysis was to provide clinical evidence regarding relationship between ADC and cellularity in different tumors based on large patient data.

Medline library was screened for associations between ADC and cell count in different tumors up to September 2016. Only publications in English were extracted. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses statement (PRISMA) was used for the research.

Overall, 39 publications with 1530 patients were included into the analysis. The following data were extracted from the literature: authors, year of publication, number of patients, tumor type, and correlation coefficients.

The pooled correlation coefficient for all studies was ρ = -0.56 (95 % CI = [−0.62; −0.50]),. Correlation coefficients ranged from ρ =−0.25 (95 % CI = [−0.63; 0.12]) in lymphoma to ρ=−0.66 (95 % CI = [−0.85; −0.47]) in glioma. Other coefficients were as follows: ovarian cancer, ρ = −0.64 (95% CI = [−0.76; −0.52]); lung cancer, ρ = −0.63 (95 % CI = [−0.78; −0.48]); uterine cervical cancer, ρ = −0.57 (95 % CI = [−0.80; −0.34]); prostatic cancer, ρ = −0.56 (95 % CI = [−0.69; −0.42]); renal cell carcinoma, ρ = −0.53 (95 % CI = [−0.93; −0.13]); head and neck squamous cell carcinoma, ρ = −0.53 (95 % CI = [-0.74; −0.32]); breast cancer, ρ = −0.48 (95 % CI = [−0.74; −0.23]); and meningioma, ρ = -0.45 (95 % CI = [−0.73; −0.17]).

Optimal experimental design for filter exchange imaging: Apparent exchange rate measurements in the healthy brain and in intracranial tumors

PURPOSE

Filter exchange imaging (FEXI) is sensitive to the rate of diffusional water exchange, which depends, eg, on the cell membrane permeability. The aim was to optimize and analyze the ability of FEXI to infer differences in the apparent exchange rate (AXR) in the brain between two populations.

METHODS

A FEXI protocol was optimized for minimal measurement variance in the AXR. The AXR variance was investigated by test-retest acquisitions in six brain regions in 18 healthy volunteers. Preoperative FEXI data and postoperative microphotos were obtained in six meningiomas and five astrocytomas.

RESULTS

Protocol optimization reduced the coefficient of variation of AXR by approximately 40%. Test-retest AXR values were heterogeneous across normal brain regions, from 0.3 ± 0.2 s-1 in the corpus callosum to 1.8 ± 0.3 s-1 in the frontal white matter. According to analysis of statistical power, in all brain regions except one, group differences of 0.3-0.5 s-1 in the AXR can be inferred using 5 to 10 subjects per group. An AXR difference of this magnitude was observed between meningiomas (0.6 ± 0.1 s-1 ) and astrocytomas (1.0 ± 0.3 s-1 ).

CONCLUSIONS

With the optimized protocol, FEXI has the ability to infer relevant differences in the AXR between two populations for small group sizes. Magn Reson Med 77:1104-1114, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

Simulations on the influence of myelin water in diffusion-weighted imaging

While myelinated axons present an important barrier to water diffusion, many models used to interpret DWI signal neglect other potential influences of myelin. In this work, Monte Carlo simulations were used to test the sensitivity of DWI results to the diffusive properties of water within myelin. Within these simulations, the apparent diffusion coefficient (D app) varied slowly over several orders of magnitude of the coefficient of myelin water diffusion (D m), but exhibited important differences compared to D app values simulated that neglect D m (=0). Compared to D app, the apparent diffusion kurtosis (K app) was generally more sensitive to D m. Simulations also tested the sensitivity of D app and K app to the amount of myelin present. Unique variations in D app and K app caused by differences in the myelin volume fraction were diminished when myelin water diffusion was included. Also, expected trends in D app and K app with experimental echo time were reduced or inverted when accounting for myelin water diffusion, and these reduced/inverted trends were seen experimentally in ex vivo rat brain DWI experiments. In general, myelin water has the potential to subtly influence DWI results and bias models of DWI that neglect these components of white matter.

Diffusion-weighted MRI findings in Sjögren's syndrome: a preliminary study

BACKGROUND

Parotid glands diffusion-weighted imaging (DWI) in Sjögren's syndrome patients have provided conflicting results currently.

PURPOSE

To determine if parotid gland DWI using a small region of interest (ROI) can provide diagnosis and assess therapeutic efficacy in Sjögren's syndrome.

MATERIAL AND METHODS

Twenty-three women with Sjögren's syndrome, five with dry mouth who did not meet diagnostic criteria for Sjögren's syndrome, and 11 healthy volunteers (controls) were evaluated with DWI. All participants received routine T1-weighted (T1W) imaging and T2-weighted (T2W) fat-suppressed imaging, and DWI. The SI ratios (SIRs) and ADC ratios (ADCRs) for parotid gland/spinal cord were then calculated. Approximately 8-10 round ROIs measuring approximately 5 mm(2) were placed on each lobe of the parotid gland, and the signal intensity (SI) was measured while avoiding fat, ducts, and blood vessels. A ROI encompassing the entire lobe of the parotid gland was also used to measure SI.

RESULTS

Using 5 mm(2) ROIs significantly higher DWI SIRs were noted in participants with Sjögren's syndrome compared with either participants with dry mouth without Sjögren's syndrome or healthy volunteers (all, P <0.001). The difference was not related to the presence of fat. No differences were noted when the larger ROI was used. In addition, parotid gland from untreated Sjögren's participants showed significantly higher SIRs compared with those from treated participants (P = 0.015).

CONCLUSION

A small ROI DWI can provide morphological and functional information on the parotid gland in Sjögren's syndrome patients, and can aid in the diagnosis and evaluation of therapeutic efficacy.

An analytical model for estimating water exchange rate in white matter using diffusion MRI

Substantial effort is being expended on using micro-structural modeling of the white matter, with the goal of relating diffusion weighted magnetic resonance imaging (DWMRI) to the underlying structure of the tissue, such as axonal density. However, one of the important parameters affecting diffusion is the water exchange rate between the intra- and extra-axonal space, which has not been fully investigated and is a crucial marker of brain injury such as multiple sclerosis (MS), stroke, and traumatic brain injury (TBI). To our knowledge, there is no diffusion analytical model which includes the Water eXchange Rate (WXR) without the requirement of short gradient pulse (SGP) approximation. We therefore propose a new analytical model by deriving the diffusion signal for a permeable cylinder, assuming a clinically feasible pulse gradient spin echo (PGSE) sequence. Simulations based on Markov Random Walk confirm that the exchange parameter included in our model has a linear correlation (R²>0.88) with the actual WXR. Moreover, increasing WXR causes the estimated values of diameter and volume fraction of the cylinders to increase and decrease, respectively, which is consistent with our findings from histology measurements in tissues near TBI regions. This model was also applied to the diffusion signal acquired from ex vivo brains of 14 male (10 TBI and 4 normal) rats using hybrid diffusion imaging. The estimated values of axon diameter and axonal volume fraction are in agreement with their corresponding histological measurements in normal brains, with 0.96 intra-class correlation coefficient value resulting from consistency analysis. Moreover, a significant increase (p = 0.001) in WXR and diameter and decrease in axonal volume fraction in the TBI boundary were detected in the TBI rats compared with the normal rats.

Numerical simulation of diffusion MRI signals using an adaptive time-stepping method

The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch-Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization is done using the explicit Runge-Kutta-Chebyshev method, which is more efficient than the forward Euler time discretization for diffusive-type problems. We use this approach to simulate the diffusion MRI signal from the extra-cylindrical compartment in a tissue model of the brain gray matter consisting of cylindrical and spherical cells and illustrate the effect of cell membrane permeability.

Investigation of field and diffusion time dependence of the diffusion-weighted signal at ultrahigh magnetic fields

Over the last decade, there has been a significant increase in the number of high-magnetic-field MRI magnets. However, the exact effect of a high magnetic field strength (B0 ) on diffusion-weighted MR signals is not yet fully understood. The goal of this study was to investigate the influence of different high magnetic field strengths (9.4 T and 14.1 T) and diffusion times (9, 11, 13, 15, 17 and 24 ms) on the diffusion-weighted signal in rat brain white matter. At a short diffusion time (9 ms), fractional anisotropy values were found to be lower at 14.1 T than at 9.4 T, but this difference disappeared at longer diffusion times. A simple two-pool model was used to explain these findings. The model describes the white matter as a first hindered compartment (often associated with the extra-axonal space), characterized by a faster orthogonal diffusion and a lower fractional anisotropy, and a second restricted compartment (often associated with the intra-axonal space), characterized by a slower orthogonal diffusion (i.e. orthogonal to the axon direction) and a higher fractional anisotropy. Apparent T2 relaxation time measurements of the hindered and restricted pools were performed. The shortening of the pseudo-T2 value from the restricted compartment with B0 is likely to be more pronounced than the apparent T2 changes in the hindered compartment. This study suggests that the observed differences in diffusion tensor imaging parameters between the two magnetic field strengths at short diffusion time may be related to differences in the apparent T2 values between the pools.

Numerical analysis of NMR diffusion measurements in the short gradient pulse limit

Pulsed gradient spin-echo (PGSE) NMR diffusion measurements provide a powerful technique for probing porous media. The derivation of analytical mathematical models for analysing such experiments is only straightforward for ideal restricting geometries and rapidly becomes intractable as the geometrical complexity increases. Consequently, in general, numerical methods must be employed. Here, a highly flexible method for calculating the results of PGSE NMR experiments in porous systems in the short gradient pulse limit based on the finite element method is presented. The efficiency and accuracy of the method is verified by comparison with the known solutions to simple pore geometries (parallel planes, a cylindrical pore, and a spherical pore) and also to Monte Carlo simulations. The approach is then applied to modelling the more complicated cases of parallel semipermeable planes and a pore hopping model. Finally, the results of a PGSE measurement on a toroidal pore, a geometry for which there is presently no current analytical solution, are presented. This study shows that this approach has great potential for modelling the results of PGSE experiments on real (3D) porous systems. Importantly, the FEM approach provides far greater accuracy in simulating PGSE diffraction data.

Sensitivities of statistical distribution model and diffusion kurtosis model in varying microstructural environments: a Monte Carlo study

The aim of this study was to investigate the microstructural sensitivity of the statistical distribution and diffusion kurtosis (DKI) models of non-monoexponential signal attenuation in the brain using diffusion-weighted MRI (DWI). We first developed a simulation of 2-D water diffusion inside simulated tissue consisting of semi-permeable cells and a variable cell size. We simulated a DWI acquisition of the signal in a volume using a pulsed gradient spin echo (PGSE) pulse sequence, and fitted the models to the simulated DWI signals using b-values up to 2500 s/mm(2). For comparison, we calculated the apparent diffusion coefficient (ADC) of the monoexponential model (b-value=1000 s/mm(2)). In separate experiments, we varied the cell size (5-10-15 μm), cell volume fraction (0.50-0.65-0.80), and membrane permeability (0.001-0.01-0.1mm/s) to study how the fitted parameters tracked simulated microstructural changes. The ADC was sensitive to all the simulated microstructural changes except the decrease in membrane permeability. The ADC increased with larger cell size, smaller cell volume fraction, and larger membrane permeability. The σstat of the statistical distribution model increased exclusively with a decrease in cell volume fraction. The Kapp of the DKI model was exclusively increased with decreased cell size and decreased with increasing membrane permeability. These results suggest that the non-monoexponential models of water diffusion have different, specific microstructural sensitivity, and a combination of the models may give insights into the microstructural underpinning of tissue pathology.

The role of tissue microstructure and water exchange in biophysical modelling of diffusion in white matter

Biophysical models that describe the outcome of white matter diffusion MRI experiments have various degrees of complexity. While the simplest models assume equal-sized and parallel axons, more elaborate ones may include distributions of axon diameters and axonal orientation dispersions. These microstructural features can be inferred from diffusion-weighted signal attenuation curves by solving an inverse problem, validated in several Monte Carlo simulation studies. Model development has been paralleled by microscopy studies of the microstructure of excised and fixed nerves, confirming that axon diameter estimates from diffusion measurements agree with those from microscopy. However, results obtained in vivo are less conclusive. For example, the amount of slowly diffusing water is lower than expected, and the diffusion-encoded signal is apparently insensitive to diffusion time variations, contrary to what may be expected. Recent understandings of the resolution limit in diffusion MRI, the rate of water exchange, and the presence of microscopic axonal undulation and axonal orientation dispersions may, however, explain such apparent contradictions. Knowledge of the effects of biophysical mechanisms on water diffusion in tissue can be used to predict the outcome of diffusion tensor imaging (DTI) and of diffusion kurtosis imaging (DKI) studies. Alterations of DTI or DKI parameters found in studies of pathologies such as ischemic stroke can thus be compared with those predicted by modelling. Observations in agreement with the predictions strengthen the credibility of biophysical models; those in disagreement could provide clues of how to improve them. DKI is particularly suited for this purpose; it is performed using higher b-values than DTI, and thus carries more information about the tissue microstructure. The purpose of this review is to provide an update on the current understanding of how various properties of the tissue microstructure and the rate of water exchange between microenvironments are reflected in diffusion MRI measurements. We focus on the use of biophysical models for extracting tissue-specific parameters from data obtained with single PGSE sequences on clinical MRI scanners, but results obtained with animal MRI scanners are also considered. While modelling of white matter is the central theme, experiments on model systems that highlight important aspects of the biophysical models are also reviewed.

Noninvasive mapping of water diffusional exchange in the human brain using filter-exchange imaging

We present the first in vivo application of the filter-exchange imaging protocol for diffusion MRI. The protocol allows noninvasive mapping of the rate of water exchange between microenvironments with different self-diffusivities, such as the intracellular and extracellular spaces in tissue. Since diffusional water exchange across the cell membrane is a fundamental process in human physiology and pathophysiology, clinically feasible and noninvasive imaging of the water exchange rate would offer new means to diagnose disease and monitor treatment response in conditions such as cancer and edema. The in vivo use of filter-exchange imaging was demonstrated by studying the brain of five healthy volunteers and one intracranial tumor (meningioma). Apparent exchange rates in white matter range from 0.8±0.08 s(-1) in the internal capsule, to 1.6±0.11 s(-1) for frontal white matter, indicating that low values are associated with high myelination. Solid tumor displayed values of up to 2.9±0.8 s(-1). In white matter, the apparent exchange rate values suggest intra-axonal exchange times in the order of seconds, confirming the slow exchange assumption in the analysis of diffusion MRI data. We propose that filter-exchange imaging could be used clinically to map the water exchange rate in pathologies. Filter-exchange imaging may also be valuable for evaluating novel therapies targeting the function of aquaporins.

A finite difference method with periodic boundary conditions for simulations of diffusion-weighted magnetic resonance experiments in tissue

A new finite difference (FD) method for calculating the time evolution of complex transverse magnetization in diffusion-weighted magnetic resonance imaging and spectroscopy experiments is described that incorporates periodic boundary conditions. The new FD method relaxes restrictions on the allowable time step size employed in modeling which can significantly reduce computation time for simulations of large physical extent and allow for more complex, physiologically relevant, geometries to be simulated.

Effect of intercompartmental water exchange on the apparent myelin water fraction in multiexponential T2 measurements of rat spinal cord

The myelin water fraction has been used as a quantitative measure of the amount of myelin present in tissue. However, recent work has suggested that intercompartmental exchange of water between myelin and nonmyelin compartments may cause the myelin water fraction to underestimate the true myelin content of tissue. In this work, multiexponential T(2) experiments were performed in vivo within the rat spinal cord, and a wide variation of the myelin water fraction (10-35%) was measured within four rat spinal cord tracts with similar myelin content. A numerical simulation based upon segmented histology images was used to quantitatively account for T(2) variations between tracts. The model predicts that a difference in exchange between the four spinal cord tracts, mediated by a difference in the average axon radius and myelin thickness, is sufficient to account for the variation in myelin water fraction measured in vivo.

Diffusion-weighted Magnetic Resonance Imaging: What Makes Water Run Fast or Slow?

Diffusion-Weighted Magnetic Resonance Imaging (DWI) obtains information useful in diagnosing several diseases through the measurement of random, Brownian diffusion of water molecules in tissues. This pictorial essay illustrates the main factors, i.e., ratio between the volume occupied by cells and the extracellular space, composition of the extracellular space, and temperature, that determine the rate of the water diffusion. The mechanism through which these influencing factors affect water diffusion is explained. Clinical and experimental examples, derived both from physiology and from non-human models, are described.

Changes in intracellular water diffusion and energetic metabolism in response to ischemia in perfused C6 rat glioma cells

This work reports results of experiments in hollow-fiber bioreactor C6 glioma cell cultures where the apparent diffusion coefficient (ADC) of intracellular water (iADC) was measured at diffusion times between 0.83 and 40 ms. The experiments were carried out before and after the onset of permanent ischemia. The changes in iADC following ischemia were dependent on the diffusion time employed in the experiment. An ischemia-induced decrease in the iADC was measured at short diffusion times, while at long diffusion times the iADC increased. Decreases in the iADC measured at short diffusion times are interpreted to be a result of a decrease in the intrinsic diffusivity of intracellular water due to energy failure. Increases in iADC measured at long diffusion times, are interpreted to result from cell swelling.

Apparent exchange rate mapping with diffusion MRI

Water exchange through the cell membranes is an important feature of cells and tissues. The rate of exchange is determined by factors such as membrane lipid composition and organization, as well as the type and activity of aquaporins. A method for noninvasively estimating the rate of water exchange would be useful for characterizing pathological conditions, e.g., tumors, multiple sclerosis, and ischemic stroke, expected to be associated with a change of the membrane barrier properties. This study describes the filter exchange imaging method for determining the rate of water exchange between sites having different apparent diffusion coefficients. The method is based on the filter-exchange pulsed gradient spin-echo NMR spectroscopy experiment, which is here modified to be compatible with the constraints of clinical MR scanners. The data is analyzed using a model-free approach yielding maps of the apparent exchange rate, here being introduced in analogy with the concept of the apparent diffusion coefficient. Proof-of-principle experiments are performed on microimaging and whole-body clinical scanners using yeast suspension phantoms. The limitations and appropriate experimental conditions are examined. The results demonstrate that filter exchange imaging is a fast and reliable method for characterizing exchange, and that it has the potential to become a powerful diagnostic tool.

Dependence of temporal diffusion spectra on microstructural properties of biological tissues

The apparent diffusion coefficient (ADC) measured using magnetic resonance imaging methods provides information on microstructural properties of biological tissues, and thus has found applications as a useful biomarker for assessing changes such as those that occur in ischemic stroke and cancer. Conventional pulsed gradient spin echo methods are in widespread use and provide information on, for example, variations in cell density. The oscillating gradient spin echo (OGSE) method has the additional ability to probe diffusion behaviors more readily at short diffusion times, and the temporal diffusion spectrum obtained by the OGSE method provides a unique tool for characterizing tissues over different length scales, including structural features of intracellular spaces. It has previously been reported that several tissue properties can affect ADC measurements significantly, and the precise biophysical mechanisms that account for ADC changes in different situations are still unclear. Those factors may vary in importance depending on the time and length scale over which measurements are made. In the present work, a comprehensive numerical simulation is used to investigate the dependence of the temporal diffusion spectra measured by OGSE methods on different microstructural properties of biological tissues, including cell size, cell membrane permeability, intracellular volume fraction, intranucleus and intracytoplasm diffusion coefficients, nuclear size and T(2) relaxation times. Some unique characteristics of the OGSE method at relatively high frequencies are revealed. The results presented in the paper offer a framework for better understanding possible causes of diffusion changes and may be useful to assist the interpretation of diffusion data from OGSE measurements.