Anomalous Diffusion Filters

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Welcome to the Anomalous Diffusion Filters Slicer Extension!

Anomalous diffusion processes (ADP) are mathematically denoted by a power law in the Fokker-Planck equation, leading to the generalized form. There are several generalizations of the Fokker-Plank equation, which should give many different partial differential equations (PDEs). Here we adopted the so-called porous media equation, allowing the super-diffusive and the sub-diffusive processes 1. In porous media, channels are created promoting or blocking the flow of the density function, which has been proved to provide a suitable application for MRI noise attenuation 2.

Basically, there are two different filters already implementing the anomalous diffusion process: the isotropic anomalous diffusion and anisotropic anomalous diffusion filters 2. These filters were already applied on different imaging MR modalities, such as structural T1 and T2 images 2, diffusion-weighted images (DWI and DTI)34, MRI relaxation T1 and T2 relaxometry5 and to fMRI6 as an initial study.

Use Cases

Most frequently used for these scenarios:

  • Use Case 1: Noise reduction as a pre-processing step for tissue segmentation

    • When dealing with single voxel classification schemes, a noise reduction pre-processing step is usually helpful to reduce data fluctuation due to acquisition artifacts (e.g. reducing the number of misclassified voxels).

  • Use Case 2: Volume rendering

    • Noise reduction will result in nicer looking volume renderings

  • Use Case 3: Noise reduction as part of image processing pipeline

    • Could offer a better segmentation and classification on specific brain image analysis such as in Multiple Sclerosis lesion segmentation

ADC map

Raw T1 weighted MRI Image

DC map

T1 weighted MRI Image with AAD filter (q=1.2)

DC map

DTI-FA map without image filtering process

DC map

DTI-FA map with AAD image filtering (q=0.4)

Cite this tool

We hope that the Anomalous Diffusion Filters can be helpful for your applications. If possible, recall to cite at least one of the following publications:

  • Da S Senra Filho, A. C., Garrido Salmon, C. E., & Murta Junior, L. O. (2015). Anomalous diffusion process applied to magnetic resonance image enhancement. Physics in Medicine and Biology, 60(6), 2355–2373. doi:10.1088/0031-9155/60/6/2355
  • Filho, A. C. da S. S., Rondinoni, C., Santos, A. C. dos, & Junior, L. O. M. (2014). Brain Activation Inhomogeneity Highlighted by the Isotropic Anomalous Diffusion Filter. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society (pp. 3313–3316). Chicago: IEEE. doi:10.1109/EMBC.2014.6944331

License

This project is under Apache version 2.0 license and following details are given at the LICENSE file in the project repository.

  1. Tsallis, C. (2009). Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World. Springer. ↩

  2. Da S Senra Filho, A. C., Garrido Salmon, C. E., & Murta Junior, L. O. (2015). Anomalous diffusion process applied to magnetic resonance image enhancement. Physics in Medicine and Biology, 60(6), 2355–2373. doi:10.1088/0031-9155/60/6/2355 ↩↩↩

  3. Senra Filho, A. C. da S., Duque, J. J., & Murta, L. O. (2013). Isotropic anomalous filtering in Diffusion-Weighted Magnetic Resonance Imaging. Conference Proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference, 2013, 4022–5. doi:10.1109/EMBC.2013.6610427 ↩

  4. Senra Filho, A. C. da S., Simozo, F. H., Salmon, C. E. G., & Murta Junior, L. O. (2014). Anisotropic anomalous filter as a tool for decreasing patient exam time in diffusion-weighted MRI protocols. In XXIV Brazilian Congress on Biomedical Engineering (pp. 0–3). Uberlandia ↩

  5. Filho, A. C. da S. S., Barbosa, J. H. O., Salmon, C. E. G. S., & Junior, L. O. M. (2014). Anisotropic Anomalous Diffusion Filtering Applied to Relaxation Time Estimation in Magnetic Resonance Imaging. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society (pp. 3893–3896). IEEE. doi:10.1109/EMBC.2014.6944474 ↩

  6. Filho, A. C. da S. S., Rondinoni, C., Santos, A. C. dos, & Junior, L. O. M. (2014). Brain Activation Inhomogeneity Highlighted by the Isotropic Anomalous Diffusion Filter. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society (pp. 3313–3316). Chicago: IEEE. doi:10.1109/EMBC.2014.6944331 ↩