Bruce Damon^{1,2}, Melissa Hooijmans^{3}, Carly Lockard^{1,2}, and Xingyu Zhou^{2,4}

^{1}Stephens Family Clinical Research Institute, Carle Health, Urbana, IL, United States, ^{2}Carle Clinical Imaging Research Program, Carle Health, Urbana, IL, United States, ^{3}Amsterdam University Medical Center, Amsterdam, Netherlands, ^{4}Biomedical Engineering, Vanderbilt University, Nashville, TN, United States

Diffusion-tensor tractography is used to quantify functionally relevant muscle architectural variables, including fiber tract length, orientation, and curvature. However, image noise and artifacts cause positional errors in the fiber tracking points and may cause tracts to terminate prematurely. The effect of the points’ positional errors on estimates of muscle fiber curvature can be mitigated through the use of polynomial fitting. Here we test several approaches for smoothing the spatial field of polynomial fitting coefficients and reconstructing missing or shortened-length fiber tracts. We show that median filtering of the polynomial coefficients retains additional fiber tracts without altering the median architectural properties.

- 2D Fitting: The distribution of coefficients across the seed point matrix is fitted to a 2-dimensional polynomial function, C = F(r,c), where r and c are the row and column positions of the seed points and the fit is weighted by using only the data from full-length tracts (Figure 1B).
- Interpolation: Missing coefficients are estimated using either nearest neighbor or natural scattered interpolation to the seed points’ X, Y, and Z positions, weighting the interpolation by using only the data from full-length tracts.
- Median filtering: The distribution of coefficients across the seed point matrix is 2D median filtered using a specified kernel size (Figure 1C)
- Gaussian filtering: The distribution of coefficients across the seed point matrix is convolved with a Gaussian function having a specified variance.

- The number of fiber tracts in the original dataset, reconstructed dataset, and merged dataset (original fiber tracts with missing fiber tracts added from the reconstructed dataset) that met the goodness criteria were computed.
- The type (3,1) intraclass correlation coefficients (ICCs) were calculated between the tracts’ curvature, pennation angle, and fiber tract length values, at the intersection of tracts populating the original and reconstructed datasets.
- The median and interquartile range were calculated for the curvature, pennation angle, and fiber tract length for the original, reconstructed, and merged datasets.
- The smoothness of spatial distributions of curvature, pennation angle, and length were computed as the mean gradients in the horizontal and vertical directions for the original, reconstructed, and merged datasets.

^{1}Lieber, R. L. & Ward, S. R.
Skeletal muscle design to meet functional demands. Philos. Trans. R. Soc. B
Biol. Sci. 366, 1466–1476 (2011).

^{2}Damon BM, Froeling M, Buck AKW, Oudeman J, Ding Z, Nederveen A, Bush EC, Strijkers GJ. Skeletal muscle DT-MRI fiber tracking: Rationale, data acquisition and analysis methods, applications, and future directions. NMR in Biomedicine. 30m e3563, doi: 10.1002/nbm.3563. (2017).

^{3}Damon, B. M., Heemskerk, A. M.
& Ding, Z. Polynomial fitting of DT-MRI fiber tracts allows accurate
estimation of muscle architectural parameters. Magn. Reson. Imaging 30,
589–600 (2012).

^{4}Damon, B. M. et al. A
MATLAB toolbox for muscle diffusion-tensor MRI tractography. J. Biomech.
124, 110540–110540 (2021).

^{5}Ding Z, Gore JC, Anderson AW. Reduction of noise in diffusion tensor images using anisotropic smoothing. Magn Reson Med 53. 485–490 (2005).

**Figure 3. Mean ICC values. **Correlations are shown

DOI: https://doi.org/10.58530/2022/2826