{ "id": "epkbtxeyqf", "slug": "diffusion-kurtosis-imaging", "title": "Diffusion kurtosis imaging", "updated": "2026-10-15", "topic_path": [ { "id": "life", "label": "Life and health", "api_url": "https://www.edgepedia.org/api/v1/topics/life" }, { "id": "life.health", "label": "Human health and medicine", "api_url": "https://www.edgepedia.org/api/v1/topics/life.health" }, { "id": "life.health.clinical", "label": "Clinical assessment and procedures", "api_url": "https://www.edgepedia.org/api/v1/topics/life.health.clinical" }, { "id": "life.health.clinical.clinical-imaging", "label": "Medical imaging and radiography", "api_url": "https://www.edgepedia.org/api/v1/topics/life.health.clinical.clinical-imaging" }, { "id": "life.health.clinical.clinical-imaging.functional-and-advanced-mri-analysis", "label": "Functional and advanced MRI analysis", "api_url": "https://www.edgepedia.org/api/v1/topics/life.health.clinical.clinical-imaging.functional-and-advanced-mri-analysis" } ], "geo": [ { "id": "geo.nongeo.t2001.life.health.clinical.clinical-imaging", "label": "Non-geographic · 2001 to 2020: Medical imaging and radiography", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.life.health.clinical.clinical-imaging", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t2001", "label": "Non-geographic · 2001 to 2020", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001" }, { "id": "geo.nongeo.t2001.life", "label": "Life and health", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.life" }, { "id": "geo.nongeo.t2001.life.health", "label": "Human health and medicine", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.life.health" }, { "id": "geo.nongeo.t2001.life.health.clinical", "label": "Clinical assessment and procedures", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.life.health.clinical" }, { "id": "geo.nongeo.t2001.life.health.clinical.clinical-imaging", "label": "Medical imaging and radiography", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.life.health.clinical.clinical-imaging" } ] } ], "excerpt": "Diffusion kurtosis imaging (DKI) is an MRI technique that quantifies non-Gaussian water diffusion in tissue, extending diffusion tensor imaging; it was introduced by Jens Jensen and colleagues in 2005.", "snippet": "Diffusion kurtosis imaging (DKI) is an MRI technique that quantifies non-Gaussian water diffusion in tissue, extending diffusion tensor imaging; it was introduced by Jens Jensen and colleagues in 2005.", "node": "life.health.clinical.clinical-imaging.functional-and-advanced-mri-analysis", "markdown": "# Diffusion kurtosis imaging\n\nDiffusion kurtosis imaging (DKI) is an MRI technique that quantifies non-Gaussian water diffusion in tissue by estimating the excess kurtosis of the diffusion-weighted signal, extending diffusion tensor imaging for microstructure characterization in neurology and oncology. It runs on clinical scanners with standard diffusion-weighted pulse sequences, requiring at least three b-values and 15 diffusion directions rather than the two b-values of conventional DWI.[1](https://pubmed.ncbi.nlm.nih.gov/20632416/) The method was introduced by Jens Jensen and colleagues in Magnetic Resonance in Medicine in 2005.[2](https://doi.org/10.1002/mrm.20508)\n\n| Key fact | Detail |\n|---|---|\n| Introducing paper | Jensen, Helpern, Ramani, Lu, and Kaczynski, Magnetic Resonance in Medicine, 2005[2](https://doi.org/10.1002/mrm.20508) |\n| Signal model | ln S(b) = ln S(0) − b·\\( D_{\\mathrm{app}} \\) + (1/6)b²·\\( D_{\\mathrm{app}} \\)²·\\( K_{\\mathrm{app}} \\)[2](https://doi.org/10.1002/mrm.20508) |\n| Kurtosis scale | \\( K_{\\mathrm{app}} \\) is unitless; 0 for Gaussian diffusion, tissue values vary and can exceed 1[3](https://onlinelibrary.wiley.com/doi/10.1002/jmri.24985) |\n| Minimum acquisition | At least 3 b-values and 15 diffusion directions[1](https://pubmed.ncbi.nlm.nih.gov/20632416/) |\n| Typical brain values | D ≈ 1 μm²/ms and K ≈ 1, implying b ≤ 3000 s/mm²[1](https://pubmed.ncbi.nlm.nih.gov/20632416/) |\n| Gray vs white matter | Mean kurtosis 0.82 ± 0.03 in gray matter, 1.41 ± 0.11 in white matter[2](https://doi.org/10.1002/mrm.20508) |\n| Main metrics | Mean kurtosis (MK), axial kurtosis (AK), radial kurtosis (RK)[4](https://www.ajronline.org/doi/10.2214/AJR.13.11365) |\n\n## How it works\n\nIn free water, displacement follows a Gaussian distribution and the diffusion-weighted signal decays as a monoexponential in b, the diffusion weighting. Tissue structure creates diffusion barriers and compartments, so displacement becomes non-Gaussian and the decay curves.[1](https://pubmed.ncbi.nlm.nih.gov/20632416/) DKI captures this with the second-order cumulant expansion of the signal:\n\n\\[ \\ln S(b) = \\ln S(0) - b \\cdot D_{\\mathrm{app}} + \\frac{1}{6} b^{2} \\cdot D_{\\mathrm{app}}^{2} \\cdot K_{\\mathrm{app}} + O(b^{3}) \\]\n\nwhere \\( D_{\\mathrm{app}} \\) is the apparent diffusivity, the first-order coefficient of the expansion, and \\( K_{\\mathrm{app}} \\) is the apparent diffusional kurtosis, the leading non-Gaussian correction; the b-factor is the usual b-value.[2](https://doi.org/10.1002/mrm.20508) \\( K_{\\mathrm{app}} \\) is unitless and equals 0 for completely Gaussian diffusion; tissue values vary by tissue, direction, and metric, and can exceed 1.[3](https://onlinelibrary.wiley.com/doi/10.1002/jmri.24985) When \\( K_{\\mathrm{app}} = 0 \\) the model reduces to the DTI model, and higher kurtosis indicates more impediments to water displacement.[4](https://www.ajronline.org/doi/10.2214/AJR.13.11365)\n\nKurtosis depends on direction, described by a tensor with 15 independent components, compared with 6 for the diffusion tensor; the full kurtosis tensor therefore requires measurements in at least 15 directions.[2](https://doi.org/10.1002/mrm.20508) For a direction n, the DIPY implementation writes the signal as S(n,b) = \\( S_{0} \\)·e^(−bD(n) + (1/6)b²D(n)²K(n)) with\n\n\\[ K(n) = \\frac{MD^{2}}{D(n)^{2}} \\sum_{i=1}^{3}\\sum_{j=1}^{3}\\sum_{k=1}^{3}\\sum_{l=1}^{3} n_{i} \\cdot n_{j} \\cdot n_{k} \\cdot n_{l} \\cdot W_{ijkl} \\]\n\nover the 15 independent elements \\( W_{ijkl} \\) of the kurtosis tensor.[5](https://docs.dipy.org/stable/examples_built/reconstruction/reconst_dki.html) The same contraction, \\( K_{\\mathrm{app}} = (MD^{2}/D^{2}) \\cdot n_{i} \\cdot n_{j} \\cdot n_{k} \\cdot n_{l} \\cdot W_{ijkl} \\), defines the apparent kurtosis coefficient from the fitted tensors.[6](https://link.springer.com/content/pdf/10.1007/s12194-013-0206-5.pdf) In white matter, AK is typically low because axial diffusion along axons is relatively free, while RK is high because cell membranes and myelin sheaths produce strongly non-Gaussian displacement.[4](https://www.ajronline.org/doi/10.2214/AJR.13.11365)\n\n## How it is done\n\nAcquisition extends a DTI protocol: at least three b-values, including two nonzero values, and at least 15 diffusion directions.[1](https://pubmed.ncbi.nlm.nih.gov/20632416/) The introducing authors' standard brain protocol uses b-values of 0, 1000, and 2000 s/mm² with 30 directions, giving whole-brain DKI in 6 min 37 s at 3T.[1](https://pubmed.ncbi.nlm.nih.gov/20632416/) Because the model adds the unknown \\( K_{\\mathrm{app}} \\), body DKI generally uses more than three b-values, including at least two above and two below 1000 s/mm².[3](https://onlinelibrary.wiley.com/doi/10.1002/jmri.24985)\n\nFitting estimates 22 parameters: \\( S_{0} \\), six diffusion-tensor elements, and 15 kurtosis-tensor elements.[7](https://pmc.ncbi.nlm.nih.gov/articles/PMC10078439/) The original paper fit the model per direction with the Levenberg–Marquardt method, using \\( S_{0} \\), \\( D_{\\mathrm{app}} \\), and \\( K_{\\mathrm{app}} \\) as free parameters.[2](https://doi.org/10.1002/mrm.20508) Ali Tabesh and colleagues later published a tensor-estimation approach for DKI in Magnetic Resonance in Medicine in 2010.[8](https://doi.org/10.1002/mrm.22655) DIPY offers weighted least squares by default and constrained or robust fitting, which is recommended to prevent physically implausible estimates, with MP-PCA denoising beforehand.[5](https://docs.dipy.org/stable/examples_built/reconstruction/reconst_dki.html) SNR matters: a minimum SNR of about 2 on the high-b-value images has been suggested for a reasonable \\( K_{\\mathrm{app}} \\) estimate,[3](https://onlinelibrary.wiley.com/doi/10.1002/jmri.24985) and inadequate SNR tends to overestimate kurtosis.[1](https://pubmed.ncbi.nlm.nih.gov/20632416/)\n\n## Origin\n\nDKI was introduced by Jens Jensen and colleagues in Magnetic Resonance in Medicine in 2005, estimating excess diffusional kurtosis in vivo with pulsed-field-gradient MRI.[2](https://doi.org/10.1002/mrm.20508) A three-dimensional characterization of non-Gaussian diffusion in humans using DKI followed in NMR in Biomedicine in 2006 by Hanzhang Lu and colleagues.[9](https://doi.org/10.1002/nbm.1020) The method built on earlier work: diffusion tensor imaging,[1](https://pubmed.ncbi.nlm.nih.gov/20632416/) generalized diffusion tensors for non-Gaussian diffusion by Chunlei Liu and colleagues in 2004,[10](https://doi.org/10.1002/mrm.20071) and the stretched-exponential model of Kevin Bennett and colleagues in 2003.[11](https://doi.org/10.1002/mrm.10581) DKI is also closely related to q-space imaging, which had been used to estimate diffusional kurtosis but demands longer imaging times, stronger gradients, and more postprocessing.[2](https://doi.org/10.1002/mrm.20508)\n\n## Variants\n\nThe most used scalar metrics are mean, axial, and radial kurtosis (MK, AK, RK), derived from the 3×3×3×3 kurtosis tensor.[4](https://www.ajronline.org/doi/10.2214/AJR.13.11365) [Kurtosis](https://www.edgepedia.org/kurtosis) fractional anisotropy (KFA) is defined through the [Frobenius norm](https://www.edgepedia.org/frobenius-norm) of the kurtosis tensor and ranges from 0 to 1 without rescaling.[12](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2017.00040/full) Directional diffusion kurtosis analysis was developed by Edward Hui and colleagues in 2008,[13](https://doi.org/10.1016/j.neuroimage.2008.04.237) and estimation of the orientation distribution function from DKI for tractography was reported by Mariana Lazar and colleagues in 2008.[14](https://doi.org/10.1002/mrm.21725) Model-based extension came with the white matter tract integrity (WMTI) model of Fieremans, Jensen, and Helpern in 2011, which combines DKI with a two-compartment intra-axonal/extra-axonal model to estimate axonal water fraction and extra-axonal tortuosity.[15](https://doi.org/10.1016/j.neuroimage.2011.06.006) Fast DKI schemes (1-3-9 and 1-9-9) need only 13 or 19 images instead of more than 60, using \\( b_{1} \\) ≈ 1 ms/μm² and \\( b_{2} \\) ≈ 2.5 ms/μm², and the 1-9-9 scheme also yields FA without extra scan time.[12](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2017.00040/full) Sub-diffusion-based mean kurtosis mapping removes the conventional ceiling on maximum b-value and uses two diffusion times without increasing acquisition time.[16](https://elifesciences.org/articles/90465) Simple diffusion kurtosis imaging (SDI) acquires DKI and ADC maps simultaneously in about 230 s using triaxial imaging and three b-values (0, 400, 800 s/mm²), against 4–7 minutes for conventional DKI.[17](https://www.mdpi.com/2075-4418/15/6/790)\n\n## Applications\n\nIn the brain, DKI has shown promising preliminary results in stroke, ADHD, glioblastoma staging, and normal aging.[15](https://doi.org/10.1016/j.neuroimage.2011.06.006) For gliomas, normalized mean kurtosis differentiated low- from high-grade lesions with 100% sensitivity and 73% specificity in one study.[4](https://www.ajronline.org/doi/10.2214/AJR.13.11365) The prostate is the most investigated extracranial organ for DKI.[3](https://onlinelibrary.wiley.com/doi/10.1002/jmri.24985) There, \\( K_{\\mathrm{app}} \\) showed higher sensitivity than ADC and \\( D_{\\mathrm{app}} \\) for tumor versus normal parenchyma (93.3% vs 78.5% and 83.5%, P<0.001),[18](https://cdn.amegroups.cn/journals/amepc/files/journals/11/articles/120163/public/120163-PB4-4378-R2.pdf) and a \\( K_{\\mathrm{app}} \\)-PSA model reached AUC 0.868 for predicting Gleason score upgrade.[18](https://cdn.amegroups.cn/journals/amepc/files/journals/11/articles/120163/public/120163-PB4-4378-R2.pdf) Body applications also include liver and kidney.[12](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2017.00040/full)\n\n## Limitations and alternatives\n\nNoise is the dominant failure mode. Without noise correction, low SNR at high b-values biases kurtosis upward, with differences between corrected and uncorrected \\( K_{\\mathrm{app}} \\) reaching about 25–30%, while \\( D_{\\mathrm{app}} \\) is affected up to about 10%.[19](https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0094531) Artifactual negative kurtosis (\"black\" voxels) can arise from noise, Gibbs artifacts, and \\( b_{0} \\) underestimation.[5](https://docs.dipy.org/stable/examples_built/reconstruction/reconst_dki.html) The cumulant model is mathematical rather than physical and applies only below \\( b_{\\mathrm{max}} = 3/(D_{\\mathrm{app}} \\cdot K_{\\mathrm{app}}) \\), the minimum of the attenuation curve; above it the model unphysically predicts increasing signal with increasing b.[20](https://cds.ismrm.org/protected/12MProceedings/PDFfiles/3560.pdf) Kurtosis estimates also lose precision rapidly if the maximum b-value falls substantially below 2000 s/mm²; fractional errors of 7–17% are typical.[2](https://doi.org/10.1002/mrm.20508)\n\nScan time is a practical cost: typical protocols acquire 60–70 images (a few b=0 images plus two 30-direction shells), too lengthy for everyday clinical use.[12](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2017.00040/full) With 21 or 22 free parameters, short protocols increase parameter variability across brain regions.[4](https://www.ajronline.org/doi/10.2214/AJR.13.11365) [Reproducibility](https://www.edgepedia.org/reproducibility) can nonetheless be good: at 1.75 mm isotropic voxels on 3T, test-retest coefficients of variation for AK, RK, and MK were generally below 4.0%, while 1.25 mm acquisition was not feasible because SNR at high b-values was insufficient.[21](https://www.nature.com/articles/s41598-017-11747-3)\n\nCompared with DTI, DKI describes the signal significantly better even at b-values commonly used for DTI. With \\( S_{0} \\) known, the DKI model has only two unknown parameters (\\( D_{\\mathrm{app}} \\) and \\( K_{\\mathrm{app}} \\)), potentially more robust than biexponential or stretched-exponential fits in noisy clinical data.[3](https://onlinelibrary.wiley.com/doi/10.1002/jmri.24985) Stretched-exponential fits, in contrast, are inconsistent with DKI and do not yield meaningful kurtosis estimates.[1](https://pubmed.ncbi.nlm.nih.gov/20632416/) Compared with q-ball imaging, DKI uses lower b-values (below 2500 s/mm²), giving better SNR plus both diffusion- and kurtosis-related parameters.[4](https://www.ajronline.org/doi/10.2214/AJR.13.11365) In prostate cancer, all high-b-value models (biexponential, kurtosis, stretched exponential, gamma distribution) achieve similar AUCs for discriminating normal from cancerous tissue,[18](https://cdn.amegroups.cn/journals/amepc/files/journals/11/articles/120163/public/120163-PB4-4378-R2.pdf) while in glioma the multicompartment models NODDI and DMI were inferior to DKI for subtype prediction under WHO 2021 classification.[22](https://pmc.ncbi.nlm.nih.gov/articles/PMC11898793/) DKI has not yet been adopted into standardized clinical protocols or guidelines.\n\n## References\n\n1. [MRI quantification of non-Gaussian water diffusion by kurtosis analysis (Jensen & Helpern, NMR in Biomedicine 2010)](https://pubmed.ncbi.nlm.nih.gov/20632416/)\n2. [Jens H. Jensen and colleagues (2005). Diffusional kurtosis imaging: The quantification of non‐gaussian water diffusion by means of magnetic resonance imaging. Magnetic Resonance in Medicine.](https://doi.org/10.1002/mrm.20508)\n3. [Body diffusion kurtosis imaging: Basic principles, applications, and considerations for clinical practice (JMRI review)](https://onlinelibrary.wiley.com/doi/10.1002/jmri.24985)\n4. [Diffusion Kurtosis Imaging: An Emerging Technique for Evaluating the Microstructural Environment of the Brain (AJR, 2014)](https://www.ajronline.org/doi/10.2214/AJR.13.11365)\n5. [Reconstruction of the diffusion signal with the kurtosis tensor model (DKI), DIPY documentation](https://docs.dipy.org/stable/examples_built/reconstruction/reconst_dki.html)\n6. [Optimization of diffusional kurtosis imaging parameters for clinical use (Radiological Physics and Technology, 2013)](https://link.springer.com/content/pdf/10.1007/s12194-013-0206-5.pdf)\n7. [Mean kurtosis-Curve (MK-Curve) correction improves the test-retest reproducibility of diffusion kurtosis imaging at 3 T](https://pmc.ncbi.nlm.nih.gov/articles/PMC10078439/)\n8. [Ali Tabesh and colleagues (2010). Estimation of tensors and tensor‐derived measures in diffusional kurtosis imaging. Magnetic Resonance in Medicine.](https://doi.org/10.1002/mrm.22655)\n9. [Hanzhang Lu and colleagues (2006). Three‐dimensional characterization of non‐gaussian water diffusion in humans using diffusion kurtosis imaging. NMR in Biomedicine.](https://doi.org/10.1002/nbm.1020)\n10. [Chunlei Liu and colleagues (2004). Characterizing non‐gaussian diffusion by using generalized diffusion tensors. Magnetic Resonance in Medicine.](https://doi.org/10.1002/mrm.20071)\n11. [Kevin M. Bennett and colleagues (2003). Characterization of continuously distributed cortical water diffusion rates with a stretched‐exponential model. Magnetic Resonance in Medicine.](https://doi.org/10.1002/mrm.10581)\n12. [Fast kurtosis imaging (Frontiers in Physics 2017, Hansen/De Santis review)](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2017.00040/full)\n13. [Edward S. Hui and colleagues (2008). Towards better MR characterization of neural tissues using directional diffusion kurtosis analysis. NeuroImage.](https://doi.org/10.1016/j.neuroimage.2008.04.237)\n14. [Mariana Lazar and colleagues (2008). Estimation of the orientation distribution function from diffusional kurtosis imaging. Magnetic Resonance in Medicine.](https://doi.org/10.1002/mrm.21725)\n15. [Els Fieremans, Jens H. Jensen, Joseph A. Helpern (2011). White matter characterization with diffusional kurtosis imaging. NeuroImage.](https://doi.org/10.1016/j.neuroimage.2011.06.006)\n16. [Robust, fast and accurate mapping of diffusional mean kurtosis (eLife, 2024)](https://elifesciences.org/articles/90465)\n17. [Improving Diagnostic Performance for Head and Neck Tumors with Simple Diffusion Kurtosis Imaging and Machine Learning Bi-Parameter Analysis (Diagnostics, 2025)](https://www.mdpi.com/2075-4418/15/6/790)\n18. [Diffusion kurtosis imaging and standard diffusion imaging in the MRI assessment of prostate cancer (Translational Andrology and Urology review)](https://cdn.amegroups.cn/journals/amepc/files/journals/11/articles/120163/public/120163-PB4-4378-R2.pdf)\n19. [Influence of Noise Correction on Intra- and Inter-Subject Variability of Quantitative Metrics in Diffusion Kurtosis Imaging (PLOS One)](https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0094531)\n20. [Optimal b-Value Range in Diffusion Kurtosis Imaging (ISMRM proceedings)](https://cds.ismrm.org/protected/12MProceedings/PDFfiles/3560.pdf)\n21. [Test-retest reliability of high spatial resolution diffusion tensor and diffusion kurtosis imaging | Scientific Reports](https://www.nature.com/articles/s41598-017-11747-3)\n22. [Performance Comparison of DKI, NODDI, and DMI in Predicting Adult-Type Glioma Subtype, A Pilot Study](https://pmc.ncbi.nlm.nih.gov/articles/PMC11898793/)\n\n---\n*Topic: Encyclopedia › Life and health › Human health and medicine › Clinical assessment and procedures › Medical imaging and radiography › Functional and advanced MRI analysis*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/diffusion-kurtosis-imaging", "markdown_url": "https://www.edgepedia.org/diffusion-kurtosis-imaging.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Diffusion kurtosis imaging\", Edgepedia (EdgeChat), https://www.edgepedia.org/diffusion-kurtosis-imaging. Edgepedia Community License 1.0.", "credit_md": "\"[Diffusion kurtosis imaging](https://www.edgepedia.org/diffusion-kurtosis-imaging)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/diffusion-kurtosis-imaging](https://www.edgepedia.org/diffusion-kurtosis-imaging). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Diffusion kurtosis imaging\", Edgepedia (EdgeChat), https://www.edgepedia.org/diffusion-kurtosis-imaging. Edgepedia Community License 1.0.", "speakable": "Diffusion kurtosis imaging is an MRI technique that quantifies non-Gaussian water diffusion in tissue, extending diffusion tensor imaging; it was introduced by Jens Jensen and colleagues in 2005." }