Introduction

Muscle architecture significantly influences muscle function¹. Therefore, accurate quantification of structural properties of muscle is essential to understanding the relationship between muscle design and performance. DTI-based fiber tractography is widely applied to study muscle architecture non-invasively². However, the outcome of structural estimates may depend on several image acquisition and analysis conditions³. Although it’s impossible to directly examine their effects in vivo, numerical simulations with known fiber geometry ground truth is one possible approach for such examination. In this work, we continue previous work³ by extending numerical simulation into 3D space and quantify the accuracy of fiber curvature (κ) estimates under different conditions of signal-to-noise ratio (S/N), voxel resolution, fiber tracking step size and polynomial fitting order to smooth fiber tracts.

Methods

Figure 1 depicts the general workflow of simulation.

Design of simulation experiments We selected percentage error of fiber curvature estimate as the criterion to evaluate architecture estimation outcomes. Table 1 lists the factors examined and their selected values in simulation. Fiber curvature was varied to represent muscle under resting state and during contraction. Image voxel size and fiber tracking step size represent the spatial frequencies of sampling and reconstruction of fiber geometry, respectively. Levels of signal-to-noise ratio (S/N) were selected to match those of voxel volumes. Effects of polynomial fitting order of fiber tracts were also examined.

Formation of model muscle Fascicles from published ultrasound images of human skeletal muscle^4–6 were digitized and fitted using previously described method³. Four levels of fascicle curvature were selected in the experiment design.

Formation of simulated image The core simulation space was constructed as 30 mm in width and depth and 120 mm in height. Muscle fibers were arranged parallel in the core space. A layer of two voxels was padded around the core space. The padded layer and voxels in core space without muscle were assumed to be occupied by adipose tissue. Diffusion tensor and image signal for each voxel were then computed using previously described method³.

Fiber tracking and smoothing Seeding points were arranged on a planar mesh perpendicular to axial plane. DTI-based fiber tractography was performed through MuscleDTI_Toolbox using commonly applied tracking options for human skeletal muscle⁷. Raw fiber tracts were smoothed by fitting them into second- and third-order polynomials.

Structural characterization To ensure consistent analysis under all conditions, fiber tracts seeding from the edge points of the planar mesh were explicitly removed. Structural properties of the remaining smoothed fiber tracts were quantified using MuscleDTI_Toolbox⁷.

Results

In each simulation run, a total of 140 simulated diffusion-weighted images were generated under 4 levels of intrinsic curvature, 7 levels of image voxel size, and 5 levels of S/N. For every simulated image, fiber tractography was performed under 4 levels of tracking step size, and each raw tract smoothed using second- and third-order polynomial fitting. Between 9 and 24 smoothed tracts remained for outcome evaluation under each condition. A total of 150 runs of simulation were performed.

Figure 2 shows the relationship between the accuracy of curvature estimate and voxel properties using second-order polynomial fitting. Briefly, image noise played the most significant role in the accuracy of curvature estimate. Tractography outcome tended to become stable with S/N > 39. For fibers with low intrinsic curvature, second-order polynomial fitting tended to overestimate the curvature, while for highly curved fibers, second-order polynomial fitting underestimated the curvature in all conditions. Lower in-plane resolution and shorter tracking step size tended to elevate the mean estimated curvature, but their effects were less significant than those from S/N.

Figure 3 illustrates a comparison between polynomial orders to fit raw fiber tracts. Overall, mean estimated curvature from third-order polynomial fitting was higher than that from second-order fitting. The accuracy of curvature estimate from third-order fitting was more sensitive to image noise, and with low intrinsic fiber curvature, third-order fitting yielded a poorer accuracy than second-order. In general, third-order polynomials fitted better for fibers with median to high curvature from images with S/N > 54.

Conclusion and Discussion

The ultimate goal of numerical simulation is to identify the nature of error in tractography and to quantify the relationship between tractography outcomes and tracking options under different conditions, so that the estimate of skeletal muscle architecture can be optimized. Using this approach, we show here the most significant determinant of the accuracy of curvature estimation is the S/N, while factors such as voxel and step sizes have relatively lesser impact. These data indicate both the need to optimize S/N when acquiring an in vivo dataset and that voxels sizes can be adjusted up to 2.00 mm × 2.00 mm × 6.0 mm in order to achieve sufficient S/N. Differences between the performance of second- and third-order polynomial fitting also indicate the need for a criterion to decide which fitting order should be used in practical applications.

Future investigations may include the introduction of variations in curvature directionality of model fibers, and application of anisotropic smoothing^8,9 in pre-processing pipeline which improves the effective S/N of diffusion-weighted images. More comprehensive criteria may also be considered to evaluate the outcome of tractography, such as the corresponding segment ratio^10,11 between model fiber and smoothed tracts, and statistical behavior of fitting residuals.

Acknowledgements

This work was supported by grant NIH/NIAMS 1 R01 AR073831.

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