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Time‐dependent diffusion MRI (td‐dMRI) has potential in characterizing microstructural features; however, its value in imaging endometrioid endometrial adenocarcinoma (EEA) remains uncertain. Patients surgically confirmed with EEA were finally enrolled in our study. The td‐dMRI data were acquired using pulsed gradient spin echo sequence and oscillating gradient spin echo sequences. The microstructural markers, including cell diameter, intracellular volume fraction (Vin), cellularity, and extracellular diffusivity (Dex), were fitted with the imaging microstructural parameters using a limited spectrally edited diffusion (IMPULSED) model. The parameters were compared between low‐ and high‐risk groups and between low‐ and high‐proliferation groups. The diagnostic performance was evaluated using receiver‐operating characteristic curve and logistic regression analysis. Diameter, Dex, ADCPGSE, ADCN1, and ADCN2 were significantly low, whereas cellularity, ΔADC1 and ΔADC2 were significantly high in the high‐risk and high‐proliferation groups. Cellularity, ΔADC1, and ΔADC2 demonstrated excellent diagnostic efficacy in predicting both risk stratification and proliferation status. Cellularity was the only independent predictor for risk stratification, which exhibited a satisfactory positive correlation with cell density in histopathologic examination. The diagnostic potential of td‐dMRI‐based microstructural mapping was demonstrated to noninvasively probe the pathologic characteristics of patients with EEA in a clinical setting, which provided a valuable contribution to surgical guidance. This work, demonstrating the diagnostic potential of td‐dMRI‐based microstructural mapping in noninvasively probing the pathologic characteristics of patients with EEA in a clinical setting and providing a valuable contribution to surgical guidance, would be of interest to a broad readership in the fields of oncology, preoperative evaluation, and cancer treatment strategies.

Preoperative differentiation of benign and malignant endometrial lesions, along with the identification of aggressive histological types of endometrial cancer (EC), is crucial for guiding treatment strategies. Time-dependent diffusion magnetic resonance imaging (TDD-MRI), which allows the characterization of tissue microstructure at the cellular level, is not currently applied for endometrial lesions. This study aimed to evaluate TDD-MRI-derived microstructural parameters for noninvasively distinguishing benign and malignant endometrial lesions and predicting aggressive histological types of EC. This prospective study enrolled 177 patients with clinically suspected EC who underwent TDD-MRI between January 2024 and March 2025. The Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion method was used to extract microstructural parameters, including the cell diameter (d), intracellular volume fraction ( ), cellularity (number of cells per unit area), cellularity index ( /d), and extracellular diffusivity ( ), along with three apparent diffusion coefficient measurements. The area under the receiver operating characteristic curve (AUC) was used to assess diagnostic performance. The Pearson correlation coefficient between the microstructural parameters and histopathological measurements was calculated. A total of 130 women (mean ± standard deviation age: 56 ± 14 years) administered uterine curettage or surgery were included in the final analysis. All microstructural parameters showed significant differences between benign endometrial lesions and EC ( < 0.05), as well as between nonaggressive and aggressive EC ( < 0.05). Cellularity exhibited the highest AUC of 0.86 for distinguishing benign endometrial lesions from EC, whereas the cellularity index showed the highest AUC of 0.88 for distinguishing aggressive histological types. D was positively correlated with ( < 0.05) and negatively correlated with diameter ( < 0.05), cellularity index ( < 0.01) and ( < 0.001) in patients with benign endometrial lesions. D was positively correlated with ( < 0.001) and negatively correlated with ( < 0.001) in patients with EC. Microstructural parameters strongly correlated with corresponding pathological features ( = 0.77-0.83; < 0.001). TDD-MRI-derived microstructural parameters demonstrated high performance in differentiating benign from malignant endometrial diseases and identifying aggressive types of EC.

The presence of micrometer-level restrictions leads to a decrease of diffusion coefficient with diffusion time. Here we investigate this effect in human white matter in vivo. We focus on a broad range of diffusion times, up to 600ms, covering diffusion length scales up to about 30 μm. We perform stimulated echo diffusion tensor imaging on 5 healthy volunteers and observe a relatively weak time-dependence in diffusion transverse to major fiber tracts. Remarkably, we also find notable time-dependence in the longitudinal direction. Comparing models of diffusion in ordered, confined and disordered media, we argue that the time-dependence in both directions can arise due to structural disorder, such as axonal beads in the longitudinal direction, and the random packing geometry of fibers within a bundle in the transverse direction. These time-dependent effects extend beyond a simple picture of Gaussian compartments, and may lead to novel markers that are specific to neuronal fiber geometry at the micrometer scale. •We measure time-dependent DTI (55 ms – 600 ms) in vivo in human white matter.•Pronounced longitudinal and weaker transverse time-dependent diffusion is observed.•Longitudinal time-dependence is attributed to axonal varicosities.•Transverse time-dependence is attributed to the random axon packing geometry.•Varying diffusion time may provide a novel microstructural contrast.

Diffusion‐weighted magnetic resonance imaging (DW‐MRI) has evolved to provide increasingly sophisticated investigations of the human brain's structural connectome in vivo. Restriction spectrum imaging (RSI) is a method that reconstructs the orientation distribution of diffusion within tissues over a range of length scales. In its original formulation, RSI represented the signal as consisting of a spectrum of Gaussian diffusion response functions. Recent technological advances have enabled the use of ultra‐high b‐values on human MRI scanners, providing higher sensitivity to intracellular water diffusion in the living human brain. To capture the complex diffusion time dependence of the signal within restricted water compartments, we expand upon the RSI approach to represent restricted water compartments with non‐Gaussian response functions, in an extended analysis framework called linear multi‐scale modeling (LMM). The LMM approach is designed to resolve length scale and orientation‐specific information with greater specificity to tissue microstructure in the restricted and hindered compartments, while retaining the advantages of the RSI approach in its implementation as a linear inverse problem. Using multi‐shell, multi‐diffusion time DW‐MRI data acquired with a state‐of‐the‐art 3 T MRI scanner equipped with 300 mT/m gradients, we demonstrate the ability of the LMM approach to distinguish different anatomical structures in the human brain and the potential to advance mapping of the human connectome through joint estimation of the fiber orientation distributions and compartment size characteristics. Linear Multi‐scale Modeling (LMM) for diffusion weighted MRI enables a detailed microstructural tissue characterization by separating orientation distributions of restricted and hindered diffusion water compartments over a range of length scales. We demonstrate the ability of LMM to estimate volume fractions, compartment sizes and orientation distributions utilizing both simulations as well as empirical data from healthy subjects using a human 3T MRI scanner equipped with a 300 mT/m gradient system.

Inferring the microstructure of complex media from the diffusive motion of molecules is a challenging problem in diffusion physics. In this paper, we introduce a novel representation of diffusion MRI (dMRI) signal from tissue with spatially-varying diffusivity using a diffusion disturbance function. This disturbance function contains information about the (intra-voxel) spatial fluctuations in diffusivity due to restrictions, hindrances and tissue heterogeneity of the underlying tissue substrate. We derive the short- and long-range disturbance coefficients from this disturbance function to characterize the tissue structure and organization. Moreover, we provide an exact relation between the disturbance coefficients and the time-varying moments of the diffusion propagator, as well as their relation to specific tissue microstructural information such as the intra-axonal volume fraction and the apparent axon radius. The proposed approach is quite general and can model dMRI signal for any type of gradient sequence (rectangular, oscillating, etc.) without using the Gaussian phase approximation. The relevance of the proposed PICASO model is explored using Monte-Carlo simulations and in-vivo dMRI data. The results show that the estimated disturbance coefficients can distinguish different types of microstructural organization of axons. •We propose a new approach for characterizing tissue microstructure using diffusion MRI that we call PICASO.•We introduce a structural disturbance function to represent inhomogeneous tissue structures.•We present the relation between the structural disturbance function and the diffusion propagators.•The structural disturbance function can be estimated using the diffusion MRI measurements.•PICASO is able to distinguish different axonal packing structures using simulations and in-vivo data.

In this article, we consider how differing approaches that characterize biological microstructure with diffusion weighted magnetic resonance imaging intersect. Without geometrical boundary assumptions, there are techniques that make use of power law behavior which can be derived from a generalized diffusion equation or intuited heuristically as a time dependent diffusion process. Alternatively, by treating biological microstructure (e.g., myelinated axons) as an amalgam of stick-like geometrical entities, there are approaches that can be derived utilizing convolution-based methods, such as the spherical means technique. Since data acquisition requires that multiple diffusion weighting sensitization conditions or b-values are sampled, this suggests that implicit mutual information may be contained within each technique. The information intersection becomes most apparent when the power law exponent approaches a value of 12, whereby the functional form of the power law converges with the explicit stick-like geometric structure by way of confluent hypergeometric functions. While a value of 12 is useful for the case of solely impermeable fibers, values that diverge from 12 may also reveal deep connections between approaches, and potentially provide insight into the presence of compartmentation, exchange, and permeability within heterogeneous biological microstructures. All together, these disparate approaches provide a unique opportunity to more completely characterize the biological origins of observed changes to the diffusion attenuated signal.

Diffusion magnetic resonance imaging (dMRI) can be used to measure a timedependent effective diffusion coefficient that can in turn reveal information about the tissue geometry. Recently, a mathematical model for the time-dependent effective diffusion coefficient was obtained using homogenization techniques after imposing a certain scaling relationship for the time, the biological cell membrane permeability, the diffusion-encoding magnetic field gradient strength, and a periodicity length of the cellular geometry. With this choice of the scaling of the physical parameters, the effective diffusion coefficient of the medium can be computed after solving a diffusion equation subject to a time-dependent Neumann boundary condition independently in the biological cells and in the extracellular space. In this paper, we analyze this new model, which we call the H-ADC model, in the case of finite domains, which is relevant to diffusion inside biological cells. We use both the eigenfunction expansion and the single layer potential representation for the solution of the above-mentioned diffusion equation to obtain analytical expressions for the effective diffusion coefficient in different diffusion time regimes. These expressions are validated using numerical simulations in two dimensions.

Objectives: To explore the feasibility of time-dependent diffusion in clinical applications of breast MRI, as well as the capacity of quantitative microstructural mapping for characterizing the cellular properties in malignant and benign breast tumors. Methods: 38 patients with 45 lesions were enrolled. Diffusion MRI acquisition was conducted with a combination of pulsed gradient spin-echo sequences (PGSE) and oscillating gradient spin-echo (OGSE) on a 3T MRI scanner. The microstructural parameters including cellularity extracellular diffusivity (Dex), mean cell size, intracellular volume fraction (νin), and the apparent diffusion coefficient (ADC) values were calculated. Each parameter was compared using the unpaired t-test between malignant and benign tumors. The area under the receiver operating characteristic curve (AUC) values was used to evaluate the diagnostic performance of different indices. Results: The mean diameter, Dex, ADC0Hz, ADC25Hz, and ADC50Hz were significantly lower in the malignant group than in the benign group (p < 0.001), while νin and cellularity were significantly higher in the malignant group (p < 0.001). All the microstructural parameters and time-dependent ADC values achieved high accuracy in differentiating between malignant and benign tumors of the breast. For microstructural parameters, the AUC of the cellularity was greater than others (AUC = 0.936). In an immunohistochemical subgroup comparison, the PR-positive group had significantly lower νin and cellularity, and significantly elevated Dex and ADC0Hz compared to the negative groups (p < 0.05). When combining diffusion parameters (cellularity, diameter, and ADC25Hz), the highest diagnostic performance was obtained with an AUC of 0.969. Conclusions: DWI with a short diffusion time is capable of providing additional microstructural parameters in differentiating between benign and malignant breast tumors. The time-dependent diffusion MRI parameters have the potential to serve as a non-invasive tool to probe the differences in the internal structures of breast lesions.

Diffusion magnetic resonance imaging (dMRI) encodes water displacement due to diffusion and is a powerful tool for obtaining information on the tissue microstructure. An important quantity measured in dMRI in each voxel is the apparent diffusion coefficient (ADC), and it is well established from imaging experiments that, in the brain, in vivo, the ADC is dependent on the measured diffusion time. To aid in the understanding and interpretation of the ADC, using homogenization techniques, we derived a new asymptotic model for the dMRI signal from the Bloch-Torrey equation governing the water proton magnetization under the influence of diffusion-encoding magnetic gradient pulses. Our new model was obtained using a particular choice of scaling for the time, the biological cell membrane permeability, the diffusion-encoding magnetic field gradient strength, and a periodicity length of the cellular geometry. The ADC of the resulting model is dependent on the diffusion time. We numerically validated this model for a wide range of diffusion times for two-dimensional geometrical configurations.